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