Logorithms on a first level learning Solve log_(5x−1)4 = 1/3

Luisottifp 2022-09-20 Answered
Logorithms on a first level learning
Solve log 5 x 1   4 = 1 / 3
( 5 x 1 ) 1 / 3 =4
( ( 5 x 1 ) 1 / 3 ) 3 = 4 3
5 x 1 = 64
5 x = 65
13
I am not sure where to go with this. I learned some things about logs before my class ended for the year. I just wanted to expand on my knowledge. This is more advance than what I am use to doing. Can someone please show me.
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Answers (2)

GrEettarim3
Answered 2022-09-21 Author has 5 answers
If I didn't understand all of the steps, I would try to include all steps. One step that is missing is explicitly raising the base to the power of the LHS and RHS respectively.
log 5 x 1 4 = 1 / 3
( 5 x 1 ) log 5 x 1 4 = ( 5 x 1 ) 1 / 3
We know that a log a Y = Y, similarly our equation becomes
4 = ( 5 x 1 ) 1 / 3
Now if 4 = ( 5 x 1 ) 1 / 3 then
4 4 4 = ( 5 x 1 ) 1 / 3 ( 5 x 1 ) 1 / 3 ( 5 x 1 ) 1 / 3
4 3 = ( 5 x 1 ) 1 / 3 + 1 / 3 + 1 / 3
64 = ( 5 x 1 ) 1 = 5 x 1

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deiluefniwf
Answered 2022-09-22 Author has 4 answers
It is easier if after the second line you cube both sides.

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