How to solve this logarithmic equation whose expressions have different bases? I have been trying to solve the following equation for a while and i can't seem to figure it out, your help would be greatly appreciated. Here is the equation: 3^x=5^(x−1)

comAttitRize8

comAttitRize8

Answered question

2022-07-19

How to solve this logarithmic equation whose expressions have different bases?
I have been trying to solve the following equation for a while and i can't seem to figure it out, your help would be greatly appreciated. Here is the equation: 3 x

Answer & Explanation

Alanna Downs

Alanna Downs

Beginner2022-07-20Added 11 answers

Hint:
log 3 ( 5 x 1 ) = ( x 1 ) log 3 ( 5 )
Tirimwb

Tirimwb

Beginner2022-07-21Added 2 answers

Here are the steps
3 x = 5 x 1
1 = 5 x 1 3 x = 5 x 1 3 x
1 = e ln ( 5 x 1 3 x ) = e ln ( 5 x 1 ) + ln ( 3 x )
ln ( 1 ) = ln ( 5 x 1 ) + ln ( 3 x )
0 = ( x 1 ) ln ( 5 ) x ln ( 3 )
ln ( 5 ) = x ln ( 5 ) x ln ( 3 )
ln ( 5 ) = x ( ln ( 5 ) ln ( 3 ) )
x = ln ( 5 ) ln ( 5 ) ln ( 3 )

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