Quiz about Algebra 2: Logarithms

Question 1

Rewrite as a logarithm.

$$6^4=1296$$

Accepted Answer

$$\log_61296=4$$

Answer

$$\log_41296=6$$

Answer

$$\log_64=1296$$

Answer

$$\log_46=1296$$

Question 2

Rewrite as a logarithm.

$$3^6=729$$

Accepted Answer

$$\log_3729=6$$

Answer

$$\log_63=729$$

Answer

$$\log_36=729$$

Answer

$$\log_6729=3$$

Question 3

Rewrite as a logarithm.

$$\left(\frac{3}{2}\right)^4=\frac{81}{16}$$

Accepted Answer

$$\log_{\frac{3}{2}}\left(\frac{81}{16}\right)=4$$

Answer

$$\log_{\frac{2}{3}}\left(\frac{16}{81}\right)=4$$

Answer

$$\log_4\left(\frac{3}{2}\right)=\frac{81}{16}$$

Answer

$$\log_{\frac{3}{2}}\left(\frac{16}{81}\right)=4$$

Question 4

Rewrite as in exponential form.

$$\log_72401=4$$

Accepted Answer

$$7^4=2401$$

Answer

$$4^7=2401$$

Answer

$$7^{-4}=2401$$

Answer

$$4^{-7}=2401$$

Question 5

Rewrite in exponential form.

$$\log_8512=3$$

Accepted Answer

$$8^3=512$$

Answer

$$3^8=512$$

Answer

$$8^{-3}=512$$

Answer

$$3^{-8}=512$$

Question 6

Rewrite in exponential form.

$$\log_216=4$$

Accepted Answer

Answer

Question 7

Rewrite as a single logarithm.

$$\log_5x+\log_5y$$

Accepted Answer

$$\log_5xy$$

Answer

$$\log_5\left(x+y\right)$$

Answer

$$\log_5\left(\frac{x}{y}\right)$$

Answer

$$\log_5\left(x-y\right)$$

Question 8

Rewrite as a single logarithm.

$$\log_x75-\log_x5$$

Accepted Answer

$$\log_x15$$

Answer

$$\log_x80$$

Answer

$$\log_x70$$

Answer

$$\log_x375$$

Question 9

Rewrite as a single logarithm.

$$\log_218+\log_25+\log_2x$$

Accepted Answer

$$\log_290x$$

Answer

$$\log_223x$$

Answer

$$\log_2\left(23+x\right)$$

Answer

$$\log_2\left(90+x\right)$$

Question 10

Rewrite as a single logarithm.

$$\log_315-\log_310-\log_3x$$

Accepted Answer

$$\log_3\left(\frac{3}{2x}\right)$$

Answer

$$\log_3\left(\frac{3}{2}x\right)$$

Answer

$$\log_3\left(\frac{3x}{2}\right)$$

Answer

$$\log_3\left(\frac{15}{10x}\right)$$

Question 11

Rewrite as a single logarithm.

$$\log_x16-\log_x14+2\log_xy$$

Accepted Answer

$$\log_x\left(\frac{8y^2}{7}\right)$$

Answer

$$\log_x\left(\frac{8}{7y^2}\right)$$

Answer

$$\log_x\left(\frac{8y}{7y}\right)$$

Answer

$$\log_x\left(\frac{8}{7}\right)$$

Question 12

Rewrite as a single logarithm.

$$\log_41.6+2\log_45-\log_4y$$

Accepted Answer

$$\log_4\left(\frac{40}{y}\right)$$

Answer

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

Answer

$$\log_416y$$

Answer

$$\log_440y$$

Algebra 2: Logarithms

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