Inverse Exponential - logarithm

What is the inverse equation for the following function? $f\left(x\right)=2\left(3\right)^x$  

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

•  $f^{-1}\left(x\right)=\log_2\left(\frac{x}{3}\right)$  

•  $f^{-1}\left(x\right)=\log_32x$  

•  $f^{-1}\left(x\right)=\log_23x$  

Tags

CCSS.HSF-BF.B.4A

What is the inverse of the function  $g\left(x\right)=2\left(3\right)^{\left(4x\right)}$  

•  $g^{-1}\left(x\right)=\frac{\log_2\left(\frac{x}{3}\right)}{4}$  

•  $g^{-1}\left(x\right)=\frac{\log_3\left(\frac{x}{2}\right)}{4}$  

•  $g^{-1}\left(x\right)=\frac{\log_3\left(\frac{x}{4}\right)}{2}$  

•  $g^{-1}\left(x\right)=\frac{\log_2\left(\frac{x}{4}\right)}{3}$  

Tags

CCSS.HSF-BF.B.4A

What is the inverse of the function  $h\left(x\right)=\ \log_3\left(\frac{x}{4}\right)-5$  

•  $h^{-1}\left(x\right)\ =\ 4\left(3\right)^{\left(x+5\right)}$  

•  $h^{-1}\left(x\right)=5\left(3\right)^{\left(\frac{x}{4}\right)}$  

•  $h^{-1}\left(x\right)=4\left(3\right)^{\left(x-5\right)}$  

•  $h^{-1}\left(x\right)=3\left(4\right)^{\left(x+5\right)}$  

Tags

CCSS.HSF-BF.B.4A

In a science experiment a scientist initially observes that there are 120 bacteria cells. One hour later the scientist observes that the cells have increased by 5%. The scientist models the growth of the number of cells with the function  $b\left(h\right)=120\left(1.05\right)^h$  , where b(x) is the number of bacteria cells and h is the number of hours. What inverse equation can predict the number of hours based on the total number of bacteria?

•  $b^{-1}\left(h\right)=\log_{1.05}\left(\frac{h}{120}\right)$  

•  $b^{-1}\left(h\right)=\log_{1.05}\left(\frac{120}{\left(h\right)}\right)$  

•  $b^{-1}\left(h\right)=\log_{120}\left(\frac{h}{1.05}\right)$  

•  $b^{-1}\left(h\right)=\log_{120}\left(\frac{1.05}{h}\right)$  

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4