2021 Module 16 Review

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

•  $\log_54$  

•  $\log_56$  

•  $\log_510$  

•  $\log_516$  

 $\log_224-\log_36$  Condense the following expression into a single logarithm:

•  $\log_34$  

•  $\log_318$  

•  $\log_330$  

•  $\log_3144$  

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  $\log_2\left(\frac{m^4}{n^7}\right)$  

•  $4\log_2m+7\log_2m$  

•  $7\log_2m+4\log_2m$  

•  $4\log_2m-7\log_2m$  

•  $7\log_2m-4\log_2m$  

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:
 $2\log\left(a\right)+4\log\left(b\right)-9\log\left(c\right)$  

•  $\log\left(a^2b^4c^9\right)$  

•  $\log\left(a^2+b^4-c^9\right)$  

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

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

Solve for x:

log₅(4x-7)=log₅(x+5)

• 3

• 12

• 4

• 7

Solve for x:

log₄(3x-1)=log₄(2x+3)

• 4

• 3

• 1

• 8

Solve for x:

log₂(x+3)=4

• 16

• 13

• 3

• 10

Solve for x:

log₂(2) + log₂(8x) = 6

• x = 3

• x = 2

• x = 6

• x = 4