Free Printable Logarithmic and Exponential Functions Test Review

1.

Solve

34=5\ln\left(x-2\right)

a)

6.

b)

898

c)

900

d)

902

2.

Solve

2\ \ln\left(x-1\right)+\ln\left(4\right)=\ln\left(10-3x\right)

a)

2

b)

$-\frac{3}{4}\ ,\ 2$

c)

$-\frac{3}{4}$

d)

$\ln\left(\frac{3}{4}\right),\ \ln\left(2\right)$

3.

Solve

e^{2x}=37

a)

1.805

b)

1.822

c)

1.931

d)

1.955

4.

Solve

\log_4\left(x\right)-\log_4\left(5\right)=\log_4\left(60\right)

a)

3

b)

12

c)

120

d)

300

5.

Choose the graph of

f\left(x\right)=2^x

a)

b)

c)

d)

6.

Choose the graph of

f\left(x\right)=3^{\left(x+1\right)}

a)

b)

c)

d)

7.

Find the balance in an account at the end of 14 years if $5000 is invested at an interest rate of 4.5% compounded continuously.

A=Pe^{rt}

a)

$9388.05

b)

$9259.72

c)

$8753.36

d)

$7841.56

8.

Evaluate

\log_4134

a)

3.533

b)

3.623

c)

3.711

d)

3.782

9.

Choose the graph of

f\left(x\right)=\log_2\left(x-1\right)

a)

b)

c)

d)

10.

In 2008, the wolf population in a certain area was 1200. The number of wolves increases exponentially at a rate of 3% per year. Predict the population in 2012.

N=N_0\left(1+r\right)^t

a)

1030

b)

1062

c)

1350

d)

1391

11.

Given

f\left(x\right)=2^x

and

g\left(x\right)=-2^{\left(x-2\right)}

, how does the graph of

g

compare to the graph of

f

?

a)

shifted 2 units to the left and reflected in the x-axis

b)

shifted 2 units to the right and reflected in the y-axis

c)

shifted 2 units to the right and reflected in the x-axis

d)

shifted 2 units to the left and reflected in the y-axis

12.

Solve $5^x=32$

a)

2.2023

b)

2.153

c)

2.241

d)

2.392

13.

Condense $\ln\left(11x\right)-5\ln\left(x\right)-4\ln\left(3y\right)$

a)

$\ln\left(\frac{11}{81x^4y^4}\right)$

b)

$\ln\left(\frac{11x^6}{3y^4}\right)$

c)

$\ln\left(\frac{81y^4}{11x^4}\right)$

d)

$\ln\left(891x^4y^4\right)$

14.

Expand $2\log_3\left(\frac{6x^2}{4y^3}\right)$

a)

$2\log_36-2\log_34-4\log_3x-6\log_3y$

b)

$2-2\log_32+4\log_3x-6\log_3y$

c)

$2\log_36+4\log_3x-6\log_34y$

d)

$4\log_3\left(6x\right)-6\log_3\left(4y\right)$

15.

$\log_4\left(\frac{1}{16}\right)$

Evaluate

a)

$-\frac{1}{2}$

b)

$\frac{1}{2}$

c)

$-2$

d)

$2$

16.

What is the amount of time required for an investment to double at a rate of 8.2% if the interest is compounded continuously? $A=Pe^{rt}$

a)

8.275 years

b)

8.453 years

c)

8.613 years

d)

8.772 years

17.

Write $4^3=64$ in logarithmic form.

a)

$\log_34=64$

b)

$\log_464=3$

c)

$\log_364=4$

d)

$\log_{64}3=4$

Logarithmic and Exponential Functions Test Review

Total questions: 17

Worksheet time: 34mins

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