Properties of Logarithms - Expanding and Condensing

Which value is equivalent to  $\log_21$ ?

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• 1

• 2

•  $\frac{1}{2}$  

Tags

CCSS.HSF.BF.B.5

Simplify the expression  $\log_66$  

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• 1

• 6

• 36

Which value is equivalent to  $\log_{11}\sqrt{11}$  

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• 1

• 2

•  $\frac{1}{2}$  

Condense the following expression into a single logarithm:
 $\log_58+\log_52$  

•  $\log_54$  

•  $\log_56$  

•  $\log_510$  

•  $\log_516$  

Condense the following expression into a single logarithm:

 $\log_324-\log_36$  

•  $\log_34$  

•  $\log_318$  

•  $\log_330$  

•  $\log_3144$  

Condense the expression
 $10\log_3x+6\log_3y$  
into a single logarithm.

•  $\log_3\left(x^{10}y^6\right)$  

•  $\log_3\left(x^{10}+y^6\right)$  

•  $\log_3\left(\ \frac{x^{10}}{\ y^6}\right)$  

•  $\log_3\left(xy\right)^{16}$  

Which expression is equivalent to  $\log_2\frac{m^4}{n^7}$  

•  $4\log_2m+7\log_2n$  

•  $7\log_2m+4\log_2n$  

•  $4\log_2m-7\log_2n$  

•  $7\log_2m+4\log_2n$  

Which expression is equivalent to  $\frac{1}{3}\ln\left(a\right)+\frac{1}{3}\ln\left(b\right)$ ?

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Expand the expression  $\log_8\left(7x^4\right)$ .

•  $\log_87+4\log_8x$  

•  $\log_87-4\log_8x$  

•  $4\log_87+4\log_8x$  

•  $4\log_87-4\log_8x$  

Condense the following expression into a single logarithm:
 $2\log\left(a\right)+4\log\left(b\right)-9\log\left(c\right)$  

•  $\log\left(a^2b^4c^9\right)$  

•  $\log\left(a^2+b^4-c^9\right)$  

•  $\log\left(\frac{a^2b^4}{c^9}\right)$  

•  $\log\left(\frac{a^2}{b^4c^9}\right)$