Solve using log. I have no idea how to use log so please explain how to use it.
Answers
Answer:
11.776
Step-by -step explanation:
Here we are given a equation which is ,
[tex]\rm\longrightarrow 10^{x-10}-8=51.7 [/tex]
And we would like to solve this using logarithms , so firstly add 8 on both sides , we get ;
[tex]\rm\longrightarrow 10^{x-10}= 51.7+8 [/tex]
Simplify,
[tex]\rm\longrightarrow 10^{x-10}= 59.7 [/tex]
Now take log to the base 10 on both sides ,
[tex]\rm\longrightarrow log_{10}10^{x-10}=log_{10}(59.7) [/tex]
Recall that [tex]log\ m^n = n\ log m [/tex] .So ;
[tex]\rm\longrightarrow (x-10)(log_{10}10=log_{10}(59.7) [/tex]
Again recall that [tex] log_a a = 1[/tex] .So ; here [tex]log_{10}10[/tex] becomes 1 .
[tex]\rm\longrightarrow (x -10)1 = log_{10}59.7 \\ [/tex]
[tex]\rm\longrightarrow (x-10)= log_{10}(59.7)[/tex]
And the value of log 59.7 = 1.7759 . So on substituting this value , we have ;
[tex]\rm\longrightarrow x -10 = 1.7759 [/tex]
Add 10 to both sides ;
[tex]\rm\longrightarrow x = 10+1.7759 [/tex]
Simplify,
[tex]\rm\longrightarrow \underline{\underline{\red{\rm { x = 11.7759 \approx 11.776}}}}[/tex]
And we are done !
[tex]\rule{200}4[/tex]
[tex]\large\red{\bigstar}\underline{\underline{\textsf{\textbf{ Some related formulae :- }}}}[/tex]
[tex]\boxed{\boxed{\begin{minipage}{5cm}\displaystyle\circ\sf\ ^{a} log \ a= 1\\\\\circ \ ^{a}log \ 1 = 0 \\\\\circ \ ^{a ^{n}} log \ b^{m}= \dfrac{m}{n} \times\:^{a}log \ b \\\\\circ \ ^{a^{m}} \ log \ b^{m} = \ ^{a}log \ b \\\\\circ \ ^{a}log \ b = \dfrac{1}{^{b}log \ a} \\\\\circ \ ^{a}log \ b = \dfrac{^{m}log \ b}{^{m} log \ a} \\\\\circ \ a^{^{a} logb} = b \\\\\circ \ ^{a}log \ b + ^{a}log \ c = \ ^{a}log(bc) \\\\\circ \ ^{a}log \ b -\: ^{a}log \ c = \ ^{a}log \left( \dfrac{b}{c} \right) \\\circ \ ^{a}log \ b \:\cdot\: ^{a}log \ c = \ ^{a}log \ c \\\\\circ \ ^{a}log \left( \dfrac{b}{c} \right) = \ ^{a}log \left(\dfrac{c}{b}\right)\end{minipage}}} [/tex]
Related Questions
Which is the estimate of 398 x 1.9?
Answers
Answer:
800
Step-by-step explanation:
When we say estimate, we must estimate the 2 numbers to their closest answer:
398- 400 when rounded to the nearest 100
1.9- 2 when rounded to the nearest whole number
So we get the estimate equation as: 400×2= 800
Solution:
We know that:
[tex]\tex\text{398 can be rounded to 400, as 398 is close to 400.}[/tex][tex]\tex\text{1.9 can be rounded to 2, as 1.9 is close to 2.}[/tex]This means that:
[tex]398 \times 1.9[/tex] ≈ [tex]400 \times 2[/tex]Simplifying "400 x 2"
[tex]400 \times 2[/tex] [tex]= 800[/tex]Thus, the estimate of 398 x 1.9 is about 800.
A semicircle is drawn onto one of the shorter sides of a rectangle. The shorter side of the rectangle measures 4 centimeters. The area of the figure is 41. 4 square centimeters. What is the length of the longer side of the rectangle?Use 3. 14 for π. Enter your answer as decimal in the box
Answers
The length of the longer side of the rectangle is 8.78cm
Area of composite figureThe formula for calculating the area of a rectangle is expressed as:
A = lw
For a semicircle;
A = πr²/2
r is the radius
Area of the figure = lw + πr²/2
Substitute the given paramters
41.4 = 4w + π(2)²/2
41.4 = 4w + 6.28
4w = 41.4 - 6.28
4w = 35.12
w = 35.12/4
w= 8.78 cm
Hence the length of the longer side of the rectangle is 8.78cm
Learn more on area of composite figure here: https://brainly.com/question/21135654
math answer? can someone help?
Answers
Answer:
I think the answer is "A"
How do i figure out the degrees?
Answers
Answer:
41°
Step-by-step explanation:
This problem involving the Law of Cosines has been mostly worked for you. The value of the cosine is the solution to the remaining one-step linear equation. The inverse cosine function (cos⁻¹ or arccos) is used to find the angle from the value of the cosine.
-1125 = -1500·cos(A)
cos(A) = -1125/-1500 = 3/4 . . . . . divide by -1500 (this is the one step)
A = arccos(3/4) ≈ 41.4096°
The angle formed by the lines to the lampposts is about 41°.
__
Additional comment
If you find the angle using the ACOS( ) function of a spreadsheet, you will always get the result in radians. Most calculators offer the choice of units for angles, so be sure you set the mode appropriately.
In the calculator screenshot, there is a decimal point in the fraction to force the angle result to be displayed as a numerical value. Otherwise, this calculator shows cos⁻¹(3/4), which isn't terribly helpful.
Write an expression to represent the perimeter of Melissa’s garden in terms of x.
Type the correct answer in each box. Use numerals instead of words.
Answers
As no diagrams attached provided the formulas which can helps you to solve by yourself
Square--4(side)Rectangle--2(Length+Breadth)Triangle--(Sum of 3 sides)Any quadrilateral--(sum of 4 sides)The expression to represent the perimeter of Melissa’s garden in terms of x is P = 8x + 14
Perimeter of a rectangleThe formula for calculating the perimeter of a rectangle is given as
P = 2(x+ y)
where;
x = 3x + 2
y = x + 5
Substitute
P = 2(3x + 2 + x + 5)
P = 2(4x + 7)
P = 8x + 14
Hence the expression to represent the perimeter of Melissa’s garden in terms of x is P = 8x + 14
Learn more on perimeter of rectangle here: https://brainly.com/question/19819849
#SPJ6
WHAT IS THE MEAN MEDIAN MODE?
Answers
Answer:
the mean is the average of a set of data the mode is the most frequent number that occurs in a set of data, and the median is the number in the middle of the set of data
Step-by-step explanation:
is 14.624777961 rational or irrational
Answers
Step-by-step explanation:
Rational number because it's terminating
find the lateral area of the figure geometry
Answers
Answer:
A) 420 in²Step-by-step explanation:
The lateral surface area excludes the area of top and bottom faces.
Given is the right pentagonal prism with side length of 7 in and height of 12 in.
The lateral area is:
L = Ph = 5*7*12 = 420 in²Correct choice is A
8. Evie buys colored
Pencils for $3.79
markers for $5.80, and
paper for $2,57, She
Pays 6.25% Sales tax.
How much does she
spend total?
Answers
Pay 12.92 in total
For a new hobby, Leo purchases a vintage camera for $475. Leo pays $5.99 for each roll he gets developed. Calculate how much Leo’s new hobby is costing him based on the number of film rolls he needs to develop.
Answers
Answer:
A = 5.99x + 475
Step-by-step explanation:
In the equation I wrote, x is equal to the number of film rolls he needs to develop. You just put that number in for x and solve the equation. That will give you the amount of money Leo spends on his new hobby.
Find the slope of the line that passes through the following points: (1,0)
and (6,-3). (Show your work.)
Answers
Answer
-3/5
Step-by-step explanation:
to find this you have to use the equation y1 - y2 / x1 - x2
so first write -3 - 0 (or 0 - - 3) over 6 - 1
it looks like -3/5
the distance covered by a spider is 5 km in 6 hours. What is its speed?
Answers
Answer:
0.83km/h
Step-by-step explanation:
v (velocity/speed) = d (distance)/t (time)
v = 5km/6h
v = 0.83km/h
please helppppppppppp
Answers
Answer:
x=√-5
Step-by-step explanation:
8-3x=√(4x^2+20)+8
-8 -8
-3x^2=√(4x^2+20)^2
-3x^2=4x^2+20
-4x^2=20
divide both sides by -4
x^2=-5
√(x^2)=√-5
x=√-5
The temperature outside changed from 94°F to 46°F over a period of eight days. If the temperature changed by the same amount each day, what was the daily temperature change?
Answers
Answer:
6°F
Step-by-step explanation:
First, subtract 46 from 94 (94-46) and you will get 48.
Then, divide 48÷8 (because the time period is 8 days) and you will get 6.
Therefore, the daily temperature change is 6°F.
I have a test tomorrow! I am trying to study. I have no clue what the difference between scale and scale factor is! How do you find them? I have to know in 20 min. Please HELP!!!
Answers
Answer:
they are similar
Step-by-step explanation:
a scale is a normal number scale while a scale factor is a scale but instead of normal numbers it uses factors
Let's see
Scale usually denotes unit rate or a numerical value change mentioned above graphs
1in=3ft.1cm=1mScale factor is same but it uses factors .
like
1/32/5What are the values of the variables in the triangle below?
Answers
Answer:
D) x=9 ; y=3√(3)
Step-by-step explanation:
[tex]Sin(30)=\cfrac{y}{6\sqrt{3} }[/tex]
[tex]\cfrac{18y}{6\sqrt{3}}=18\sin \left(30^{\circ \:}\right)[/tex]
[tex]\sqrt{3}y=9[/tex]
[tex]\cfrac{\sqrt{3}y}{\sqrt{3}}=\cfrac{9}{\sqrt{3}}[/tex]
[tex]y=3\sqrt{3}[/tex]
~
[tex]Cos(30)=\cfrac{x}{6\sqrt{3} }[/tex]
[tex]\cfrac{18x}{6\sqrt{3}}=18\cos \left(30^{\circ \:}\right)[/tex]
[tex]\sqrt{3}x=9\sqrt{3}[/tex]
[tex]\cfrac{\sqrt{3}x}{\sqrt{3}}=\cfrac{9\sqrt{3}}{\sqrt{3}}[/tex]
[tex]x=9[/tex]
Therefore, x=9 and y=3√(3)
~
How many liters are there in a tank of volume 7.32m³?
Answers
Answer: 3 liters in a tank of volume 7.32m^3
Step-by-step explanation:
Which of the following expressions are equivalent to 4^-3/4^-8? Check all that apply.
4^8/4^3
4^-8/4^-3
4^-5
4^5
Answers
Answer: 4^5
Step-by-step explanation:
4^5. when you divide exponents you just subtract them, so -3-(-8) is 5.
A recipe uses 5 cups of milk to make 20 servings. If the same amount of milk is used for each serving, how many servings can be made from three quarts?
Answers
Naelly is taking a class trip to Washington DC. The cost of the trip is $459. 60. Naelly paid an initial deposit of $150, and must make the remainder of the payments in 12 equal monthly payments. What is the amount of each monthly payment in dollars and cents?
Answers
459.6 - 150 = 309.6
309.6 / 12 = $25.80 a month for 12 months
Bananas cost $0.50 each, and apples cost $1.00 each.
(a) Elena would like to spend exactly $3.50 on buying fruits. If she buys 1 banana, how
many apples can she buy?
(b) Is it possible for Elena to buy 2 bananas, if she wants to spend exactly $3.50? Why or
why not?
Answers
Answer:
(a) 3 apples (b) no
Step-by-step explanation:
(a) 1 bannana = 0.50
3 apples = 3.00
total = 3.50
(b) Not possible because 2 bannanas = 1 dollar 3 bananas = 1.50 then 1.50 + 2.00 apples = 3.50
Downtown it snowed 1/10 of an inch inthe morning and 3/10 of an inch in the evening. How much more snow fell in the evening than in the morning?
Answers
Answer:
2/10
Step-by-step explanation:
Keep the bases the same so we are dealing with 3 - 1 so we get 2. 2/10 of snow falls in the evening than in the morning.
Have an amazing day!
PLEASE RATE!!!
3. Find the geometric mean of 4 and 10. (1 point) A. 20 B. 7 C. SQ root of 14 D. 2x SQ root of 10
Answers
Answer:
[tex]2\sqrt10[/tex]
6.3 to the nearest 10th
Step-by-step explanation:
Hope this helped :)
please solve: -15=x-16
Answers
Answer:
-15=x-16
x-16= -15
x= -15+16
x=1
Ms. Pierce bought a camera that cost $450. She also had to pay an additional 5% sales tax. How much did Ms. price pay for the camera
Answers
the price, right? Remember that "percent"
means for each 100, so 104% = 104/100 :
1.04. 1.04(450) = $468.
Kevin plants a total of 72 flowers in equal rows. He plants 6 rows of yellow flowers and 2 rows of red flowers. How many flowers are in each row.
Answers
Answer:
72 +6+2 equal80
Step-by-step explanation:
have to pluse all
HELP! QUICK!
Find the length and width of rectangle CBED, and calculate its area.
Answers
Answer:
170 units
Step-by-step explanation:
60+60+25+25=170
The 60 and 60 can be found by adding the length, 20+35+5.
The 25 and 25 can be found by taking 55+8-(30+8) for the widths.
Answer:
Step-by-step explanation:
Length = DE =OP
OP = 5 + 20 + 35 = 60 ft
Length of the rectangle CBED = 60ft
Width CD = CJ - (DG +GJ)
= 55 - (8 + 30)
= 55 - 38
= 17 ft
Area of CBED = length * width
= 60 * 17
= 1020 ft²
4s^3 when s=2
plsss help
Answers
Answer:
32
Step-by-step explanation:
=> 4s[tex]{}^{3} [/tex]
=> 4(2)[tex]{}^{3} [/tex]
=> 4(2×2×2)
=> 4(8)
=> 32
Please answer this friends ?
Answers
Answer: Rs. 6075
40500×(15/100)= 6075
Step-by-step explanation:
Nicholas has a collection of books. He has 115 fantasy and science fiction books. These books are 46℅ of his collection. How many books does he have in his collection?
-- pls explain!!!
Answers
Answer:
46% of 115 gives 52.9 because it is the total of books that is not given