Question

Solve below log Equation, this equation came with different bases:log2(x+2)-3*log8(x+3)=2

Logarithms
ANSWERED
asked 2020-12-03

Solve below log Equation, this equation came with different bases: \(\displaystyle{\log{{2}}}{\left({x}+{2}\right)}-{3}\cdot{\log{{8}}}{\left({x}+{3}\right)}={2}\)

Answers (1)

2020-12-04
\(\displaystyle{\log{{2}}}{\left({x}+{2}\right)}-{3}\cdot{\log{{8}}}{\left({x}+{3}\right)}={2}\)
\(\displaystyle{8}={2}^{{3}},\ {s}{o}\ {\log{{8}}}={\left(\frac{{1}}{{3}}\right)}{\log{{2}}}\)
\(\displaystyle{\log{{2}}}{\left({x}+{2}\right)}-{\log{{2}}}{\left({x}+{3}\right)}={2}\)
\(\displaystyle{\log{{2}}}{\left[\frac{{{x}+{2}}}{{{x}+{3}}}\right]}={2}\)
thus, \(\displaystyle\frac{{{x}+{2}}}{{{x}+{3}}}={2}^{{2}}={4}\)
x+3=4*(x+3)
x+3=4x+12
3x=3-12=-9
x=-3
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