Equation with Logarithm: \(\displaystyle{{\log}_{{x}}{3}}+{{\log}_{{x}}{12}}={2}\) How do I solve it?

Harley Ayers

Harley Ayers

Answered question

2022-04-04

Equation with Logarithm:
logx3+logx12=2
How do I solve it? My idea was to use the formula loga(b)=lnblna but that does not seem to help here.

Answer & Explanation

LiaisyAciskriuu

LiaisyAciskriuu

Beginner2022-04-05Added 10 answers

logx3+logx12=logx(3×12)=logx36
Boehm98wy

Boehm98wy

Beginner2022-04-06Added 18 answers

Your method is feasible indeed! Using the formula, logab=lnalnb, we get
ln3lnx+ln12lnx=2
ln3+ln12lnx=2
ln(3×12)lnx=2
lnx=12×ln36
lnx=ln{3612}
lnx=ln6
x=6

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