How do you find the inverse of y = 1 + log_10 (x + 2) ?

1 Answer
Oct 10, 2015

f^-1(x)=(10^x-20)/10

Explanation:

1 can be written as log_10 10.

y= log_10 10+log_10 (x+2)

Using the Product Law which states that log_b AC= log_b A+ log_b C,

y=log_10 (10*[x+2])
y=log_10 10x+20

Since log_a b=c can be written as b=a^c,

10x+20=10^y

Make x the subject.
10x=10^y-20
x=(10^y-20)/10

Change y to x in your final answer.

f^-1(x)=(10^x-20)/10