Properties of logs review

Properties of Logs Review

Match

Match each equation in logarithmic form to the corresponding exponential form.

• $$\log_2 8 = x$$

• $$\log_5 125 = x$$

• $$\log_2x=8$$

• $$\log_4 64 = x$$

• $$\log_5x=125$$

• $$2^x = 8$$

• $$5^x = 125$$

• $$2^8=x$$

• $$4^x = 64$$

• $$5^{125}=x$$

Categorize

Options (8)

$$3\cdot\log_24$$  

$$\log12+\log7$$  

$$\log_79-\log_73$$  

$$\log_5x^3$$  

$$\ln\left(x^2+2x+2\right)$$  

$$\log_8\left(\frac{3}{2}\right)$$  

$$\log_2x-\log3$$  

$$\log_2\left(x+2\right)$$  

Organize the logarithms based on which property would be used to expand or compress them.

Power proerty

Product Property

Quotient Property

Can't be condensed/ expanded

Math Response

Write the logarithm in exponential form:

$$\log_ba=x$$

Type answer here

Correct Answer: b^x=a

Deg^°

Rad

Multiple Choice

Evaluate the logarithm:

$$\log_216$$

• 8

• 4

• 32

• 2

Multiple Choice

Evaluate the Logarithm:

$$\log_327$$

• 3

• 9

• 81

• 12

Math Response

Evaluate the logarithm using the change of base formula: (round to two decimal places)

$$\log_512$$

Type answer here

Correct Answer: 1.54

Deg^°

Rad

Math Response

Use the properties of logs to compress the expression:

$$2\cdot\log_4x+4\cdot\log_4x$$

Type answer here

Correct Answer: \log_4\left(x^6\right)

Deg^°

Rad

Math Response

Use the Properties of logarithms to compress the expression:

$$\log\left(x+1\right)-\log\left(x\right)+\log\left(x-1\right)$$

Type answer here

Correct Answer: \log\left(\frac{x^2-1}{x}\right)

Deg^°

Rad

Math Response

Use the properties of logarithms to compress the expression:

$$2\cdot\ln4-\frac{1}{2}\left(\ln27-\ln3\right)$$

Type answer here

Correct Answer: \ln\left(\frac{16}{3}\right)

Deg^°

Rad

Math Response

Use the properties of logarithms to expand the expression completely:

$$\log_2\left(x^2+2x+1\right)$$

Type answer here

Correct Answer: 2\log_2\left(x+1\right)

Deg^°

Rad

Math Response

Use the properties of logarithms to expand the expression completely:

$$\log\left(\frac{3x^3}{5}\right)$$

Type answer here

Correct Answer: \log\left(3\right)+3\log\left(x\right)-\log\left(5\right)

Deg^°

Rad

Math Response

Use the properties of logarithms to expand the expression completely:

$$\log_6\left(\frac{2x^2-5x-3}{\sqrt[3]{12x}}\right)$$

Type answer here

Correct Answer: \log_6\left(2x+1\right)+\log_6\left(x-3\right)-\frac{1}{3}\left(\log_6\left(12\right)+\log_6\left(x\right)\right)

Deg^°

Rad

Multiple Choice

Use the properties of logs to find $$\log_44200$$ without a calculator given the log values:

$$\log_46=1.3$$

$$\log_410=1.7$$

$$\log_47=1.4$$

• 6.02

• 4.4

• 3.62

• 6.1