Logarithmic Functions and Properties

The base of the common log,

 $\log_{ }x$  is:

• 10

• e

• 5

• 100

The base of the natural log,

 $\ln x$  is:

• 10

• e

• 5

• 100

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

Convert the exponential expression into an equivalent logarithmic expression:

 $3^x=7$  

•  $\log_37=x$  

•  $\log_3x=7$  

•  $\log_73=x$  

•  $\log_x7=3$  

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

Convert the exponential expression into an equivalent logarithmic expression:

 $2^{x-2}=11$  

•  $\log_211=x-2$  

•  $\log_2\left(x-2\right)=11$  

•  $\log_{11}2=x-2$  

•  $\log_{x-2}11=2$  

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

Convert the exponential expression into an equivalent logarithmic expression:

 $3^{3x}=9$  

•  $\log_39=3x$  

•  $\log_93=3x$  

•  $\log_{3x}9=3$  

•  $\log_93x=3$  

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

Convert the logarithmic expression into an exponential expression:

 $\log_34x=7$  

•  $3^7=4x$  

•  $3^{4x}=7$  

•  $\left(4x\right)^7=3$  

•  $7^3=4x$  

Tags

CCSS.HSF.BF.B.5

Convert the logarithmic expression into an exponential expression:

 $\log\left(2x-3\right)=2$  

•  $10^2=2x-3$  

•  $2^{10}=2x-3$  

•  $10^{2x-3}=2$  

•  $\left(2x-3\right)^2=10$  

Tags

CCSS.HSF.BF.B.5

Convert the logarithmic expression into an exponential expression:

 $\ln\left(x+4\right)=7$  

•  $e^7=x+4$  

•  $e^{x+4}=7$  

•  $\left(x+4\right)^e=7$  

•  $7^e=x+4$  

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

Find the equivalent logarithmic expression:

 $\log\left(x\times y\times z\right)$  

•  $\log x+\log y+\log z$  

•  $\log x-\log y-\log z$  

•  $\log x-\log y+\log z$  

•  $\log x+\log y-\log z$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Find the equivalent logarithmic expression:

 $\log3+\log a+\log b$  

•  $\log\left(3ab\right)$  

•  $\log\left(\frac{3a}{b}\right)$  

•  $\log\left(\frac{3}{ab}\right)$  

•  $\log\left(\frac{1}{3ab}\right)$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3