Answer:
\(y=log_6(x)\)
Step-by-step explanation:
the inverse of \(y=6^x\)
To find inverse , we swap the variables. Replace x with y and y with x
\(x=6^y\)
Now solve for y
To solve for y , take log on both sides
\(log x= log(6^y)\)
Move the exponent y before log as per the log property
\(log x= y log(6)\)
Divide both sides by log 6
\(y=\frac{logx}{log6}\)
Apply change of base formula to get single log
\(y=log_6(x)\) is the inverse function
