The inverse function of a logarithm equation I've tried many things with this question, and just c

Justine Webster

Justine Webster

Answered question

2022-05-15

The inverse function of a logarithm equation
I've tried many things with this question, and just can't seem to get it quite right, can someone please show me how to answer this question? Thank you in advance.
g ( x ) = ln ( 5 x + 25 ) g 1 ( x ) = X X e x X X X

Answer & Explanation

Haylie Cherry

Haylie Cherry

Beginner2022-05-16Added 17 answers

To find the inverse, I would let g ( x ) = y, then solve for x in terms of y. After that, I would swap x and y, then replace y with g 1 ( x ). We have our function:
g ( x ) = ln ( 5 x + 25 )
First, rewrite with log e instead of ln.
g ( x ) = log e ( 5 x + 25 )
Make the substitution g ( x ) = y.
y = log e ( 5 x + 25 )
Remember that if log a ( b ) = x, then a x = b
e y = 5 x + 25
Solve for x
5 x = e y 25
x = e y 25 5
Swap x and y
y = e x 25 5
Change y into g 1 ( x )
g 1 ( x ) = e x 25 5
g 1 ( x ) = e x 5 5
Govindennz34j

Govindennz34j

Beginner2022-05-17Added 6 answers

To find the inverse of the function g ( x ) = ln ( 5 x + 25 ), solve for x
g = ln ( 5 x + 25 ) e g = 5 x + 25 x = e g 25 5
g 1 ( x ) = e x 25 5 = 1 5 e x 5

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