Free Printable 5.2 Solving Exponential Equations/5.3 Inverses Practice

1.

Oliver, Noah, and Rohan are on a treasure hunt. They come across a mysterious door with a lock that can only be opened by solving a riddle. The riddle is:

Find the value of x for

$5^{\left(2x+3\right)}=\frac{1}{125}.$

Can you help them unlock the door?

(a)

2.

Solve the equation. Round your answer to the nearest ten-thousandth. $18^x=50.9$

a)

1.3596

b)

1.7067

c)

3.9299

d)

No solution

3.

Solve the equation. Round your answer to the nearest ten-thousandth. $14^{3x}=63.7$

a)

1.3669

b)

0.6014

c)

1.3847

d)

0.5247

4.

Henry, Elijah, and Liam are on a treasure hunt. They found a mysterious box with a lock that can only be opened by solving the equation for x. Can you help them?

a)

-0.659

b)

-0.528

c)

-2.159

d)

-0.478

5.

Daniel, Abigail, and Michael are on a treasure hunt. They found a map with the number 435.86 written on it. To unlock the treasure, they need to round this number to the nearest tenth. Can you help them?

(a)

6.

Scarlett is calculating the cost of her shopping trip and the total comes to $3,999.243. What is the total cost rounded to the nearest hundredth?

a)

$3,999.24

b)

$3,999.25

c)

$3,999.244

d)

$3,400.00

7.

Round to the nearest whole number.
77.538

a)

100

b)

77

c)

78

d)

77.5

8.

Round to the nearest whole number:
14.08

a)

14.08

b)

14

c)

15

d)

14.8

9.

What is 9.0294 rounded to the nearest hundredth?

(a)

10.

If $f\left(x\right)=10^x$ ,then the inverse function is which function below?

a)

$f^{-1}\left(x\right)=10^{2x}$

b)

$f^{-1}\left(x\right)=\log_{10}x$

c)

$f^{-1}\left(x\right)=\log_x10$

d)

$f^{-1}\left(x\right)=\log10$

11.

If $f\left(x\right)=\left(4\right)^x$ ,then the inverse function is which function below?

a)

$f^{-1}\left(x\right)=4^{2x}$

b)

$f^{-1}\left(x\right)=\log_4x$

c)

$f^{-1}\left(x\right)=\log_x4$

d)

$f^{-1}\left(x\right)=\log4$

12.

Convert the following expression to exponential form: $\log_5a=b$ can be written as (a)

Choose from the below words

a=b^5

a=5^b

5=a^b

b=5^a

13.

Which of the following is the inverse of $\log_3\left(d\right)=c$

a)

$3^d=c$

b)

$3^c=d$

c)

$c^3=d$

d)

$d^3=c$

14.

Solve for x (round your answer to the hundredths place)

$16^{\left(x-7\right)}+5=24$

(a)

15.

Solve the following for x (Round to the thousandths place)

$10^{\left(x-2\right)}=15$

(a)

16.

Solve for x (Round to the hundredths place)

$4^{\left(x-3\right)}+1=30$

(a)

17.

Rohan is trying to calculate the amount of time it takes for a chemical reaction to occur. He found the equation representing the reaction as: $20^{-5a}-6=37$ Where 'a' represents the time in minutes. Help Rohan solve the equation and find the time 'a' rounded to the nearest ten-thousandth.

a)

-0.2511

b)

-0.7522

c)

-0.3267

d)

-0.7907

5.2 Solving Exponential Equations/5.3 Inverses Practice

Total questions: 17

Worksheet time: 45mins

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