Condense and Expand Logs

Condense $15\ \log_5a\ +3\ \log_5b$  

•  $15\log_5ab$  

•  $\log_5\left(a^{15}b^3\right)$  

•  $\log_5\left(b^{15}a^3\right)$  

•  $45\log_5\left(ab\right)$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

 $4\log_4u-6\log_4v$  Condense

•  $\log_4\left(\frac{u}{v}\right)^{24}$  

•  $\log_4\left(\frac{u^6}{v^4}\right)^{ }$  

•  $\log_4\left(\frac{u^4}{v^6}\right)^{ }$  

•  $\log_4\left(\frac{v^6}{u^4}\right)^{24}$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.LE.A.4

Expand $\log_4\left(x^5y^2\right)$  

•  $10\log_4\left(x\ +y\right)$  1

•  $5\log_4x+2\log_4y$  

•  $5\log_9x+2\log_9y$  

•  $\log_4\left(5x+2y\right)$  

Tags

CCSS.HSF.BF.B.5

 $Expand\ \log_5\left(xy^5\right)^2$  

•  $2\log_5x\ +10\log_5y$  

•  $10\left(\log_5x\ +\log_5y\right)$  

•  $10\log_5x\ +10\log_5y$  

•  $10\log_5x\ +2\log_5y$  

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

CCSS.HSF.LE.A.4

Write the log in exponential form
 $\log_5y=2$  

•  $5^y=2$  

•  $2^5=y$  

•  $2^y=5$  

•  $5^2=y$  

Tags

CCSS.HSF.BF.B.5

Write in a log form
 $3^5=y$  

•  $\log_3y=15$  

•  $\log_5y=3$  

•  $\log_3y=3$  

•  $\log_3y=5$  

Tags

CCSS.HSF.BF.B.5

Expand the Log completely and simplify if possible.  $\log_{ }\left(\frac{\sqrt{x}}{z^5y}\right)$  

•  $\frac{1}{2}\log x\ -5\log z-\log y$ 

•  $\log\ x^{\frac{1}{2}\ }-\log\ z^5+\log\ y$  

•  $\log\ \sqrt{x}-\log z^5+y^{ }$   

•  $10\log\ x-z+y$  

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

Expand the Log completely and simplify if possible.  $\log_{ }8x^3$  

•  $\log8\ +3\log x$ 

•  $\log\ 8+\log\ x^3$  

•  $.9+3\log x$   

•  $3\log8x$  

Expand the Log completely and simplify if possible.  $\log\left(xyz\right)^4$  

•  $4\log x\ +4\log y+4\log z$ 

•  $4\log\ xyz$  

•  $4\log\ x+y+z$   

•  $4\log\ x+\log y+\log z$  

Condense the Log completely and simplify if possible.  $7\log x+y\log z$  

•  $\log x^7z^y$ 

•  $\log\ x^7+\log\ z^y$  

•  $7y\ \log x+z$   

•  $\log7x+yz$