Quick Log problem? 2(x^3)=3(x^2) Solve for x I'm pretty sure I use logs to solve this, but how? to what base? I'm kinda lost.. Thanks

Meldeaktezl

Meldeaktezl

Answered question

2022-09-09

Quick Log problem?
2 ( x 3 ) = 3 ( x 2 )
Solve for x
I'm pretty sure I use logs to solve this, but how? to what base? I'm kinda lost.. Thanks

Answer & Explanation

Haylee Branch

Haylee Branch

Beginner2022-09-10Added 7 answers

Taking logs to any base,
x 3 log 2 = x 2 log 3   ,
and therefore either x = 0 or x = ( log 3 ) / ( log 2 ). Note that by the "change of base" formula, the last expression is the same no matter what base you are using.
ivybeibeidn

ivybeibeidn

Beginner2022-09-11Added 2 answers

Take natural log
2 x 3 = 3 x 2 x 3 ln 2 = x 2 ln 3 x 2 ( x ln 2 ln 3 ) = 0 x 1 , 2 = 0 ,   x 3 = ln 3 ln 2 = log 2 3

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