Free Printable Exponential and Logarithmic Equations

1.

The following is considered a logarithmic equation: $\log_464x^3$

a)

True

b)

False

2.

According to the logarithmic properties: $e^{\ln x}=x$

a)

True

b)

False

3.

The following is considered an exponential equation: $5^x=1.4$

a)

True

b)

False

4.

The following is considered a logarithmic equation: $2\ln3x=8$

a)

True

b)

False

5.

According to the change of base property: $\log_672,348=4.86$

a)

True

b)

False

6.

Use the logarithmic properties to expand the expression correctly: $\log_3\ \frac{∛x}{81}$

a)

$\log x-\log81_{ }$

b)

$\log_3x+\log_381$

c)

$3\log_3x+4$

d)

$\frac{1}{3}\log_3x-4$

7.

Use the logarithmic properties to condense the expression correctly. $6\log x+2\log y$

a)

$\log x^6y^2$

b)

$\log_6x\log_2y$

c)

$\log\frac{x^6}{y^2}$

d)

$12\log xy$

8.

Find the solution to the exponential equation: $e^{12-5x}-7=123$

a)

3.161

b)

1.426

c)

1.136

d)

0.036

9.

The formula $A=10.1e^{0.005t}$ models the population of Los Angeles, California in millions, t years after 1992. If the growth rate continues into the future, when will the population reach 13 million?

a)

In the year 2042

b)

In the year 2000

c)

In the year 2213

d)

In the year 2504

10.

The Energy (in ergs) liberated during an earthquake of magnitude R can be calculated through the formula $\log⁡E=11.4+1.5R$ Find the Energy liberated during an earthquake of an 8.4 magnitude on the Richter scale.

a)

$2.5x10^9ergs$

b)

0.924 ergs

c)

$1x10^{24}ergs$

d)

1.38 ergs

Exponential and Logarithmic Equations

Total questions: 10

Worksheet time: 1hrs 20mins

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