Question

Which of the following is the inverse of y=12^x

Answer 1

`y = (\log x)/(\log 12)`

Explanation:

`y = 12^x`

`x = 12^y`

`\log x = \log 12^y`

`\log x = y \log 12`

`y \log 12 = \log x`

`y = (\log x)/(\log 12)`

Answer 2

`y=12^x\ \ \ |log_(12)\\\\\log_(12)y=\log_(12)12^x\\\\\log_(12)y=x\log_(12)12\\\\x=\log_(12)y`



`y=12^x\to y^(-1)=\log_(12)x;\ x\in\mathbb{R^+}\to\ y^(-1)=(\log x)/(\log12);\ x\in\mathbb{R^+}\to y^(-1)=(\ln x)/(\ln 12)`


`Used:\\\\\log_aa=1\\\\\log_ab^n=n\log_ab\\\\\log_ab=(\log_cb)/(\log_ca)`