late 5.5 Inverse of Exponential Functions

evaluate:

 $\log_232=$ 

2 to what power = 32 ?

(a)  

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CCSS.HSF.BF.B.5

evaluate:

 $\log_216=$ 

2 to what power = 16 ?

(a)  

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CCSS.HSF.BF.B.5

evaluate:

 $\log1000=$ 

10 to what power = 1000 ?

(a)  

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CCSS.HSF.BF.B.5

Rewrite in Logarithmic notation

 $7^3=343$  

•  $\log_7343=3$  

•  $\ln343=7$  

•  $\log_{343}7=3$  

•  $\log_3343=7$  

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CCSS.HSF.BF.B.5

Rewrite in Logarithmic notation

 $5^6=3125$  

•  $\log_53125=6$  

•  $\log3125=5$  

•  $\log_{3125}5=6$  

•  $\log_63125=5$  

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CCSS.HSF.BF.B.5

Rewrite in Logarithmic notation

 $3^x=27$  

•  $\log_327=x$  

•  $\ln27=x$  

•  $\log_{27}3=x$  

•  $\log\left(27x\right)=3$  

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CCSS.HSF.BF.B.5

Rewrite in Logarithmic notation

 $10^2=100$  

•  $\log100=2$  

•  $\ln100=2$  

•  $\log_{100}2=10$  

•  $\log_2100=10$  

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CCSS.HSF.BF.B.5

To find the inverse of

 $f\left(x\right)=3^x+2$ 

you would first switch the x and y's and get the base alone 

•  $x+2=3^y$  

•  $x-2=3^y$  

•  $\frac{x}{3}=y+2$  

•  $x+3=2^y$  

Tags

CCSS.HSF-BF.B.4A

 $x-2=3^y$  
then you would rewrite it as a logarithm and get y by itself and replace y with  $f^{-1}\left(x\right)$  

•  $f^{-1}\left(x\right)=\log_3\left(x-2\right)$  

•  $f^{-1}\left(x\right)=\log_3\left(x+2\right)$  

•  $f^{-1}\left(x\right)=\ln\left(x-2\right)$  

•  $f^{-1}\left(x\right)=\log\left(x-2\right)$  

Tags

CCSS.HSF-BF.B.4A

To find the inverse of

 $f\left(x\right)=2\left(3\right)^x$ 

you would first switch the x and y's and get the base alone 

•  $\frac{1}{2}x=3^y$  

•  $x-2=3^y$  

•  $\frac{x}{3}=y^2$  

•  $x+2=3^y$  

Tags

CCSS.HSF-BF.B.4A