Answer: [tex]y=\frac{ln(x)}{ln(10)}[/tex]
Step-by-step explanation:
To find the inverse of the function, you first replace the y with x and x with y. Then you solve for y.
[tex]y=10^x[/tex] [replace y with x and x with y]
[tex]x=10^y[/tex] [find natural log of both sides to get y alone]
[tex]ln(x)=ln(10)^y[/tex] [divide ln(10) on both sides]
[tex]\frac{ln(x)}{ln(10)} =y[/tex]
Now that we have found y after switching y with x and x with y, we know that the inverse is [tex]y=\frac{ln(x)}{ln(10)}[/tex].
