Question

log (x + 5) - log (x - 3) = log 2

Logarithms
ANSWERED
asked 2020-10-19
\(\displaystyle{\log{{\left({x}+{5}\right)}}}-{\log{{\left({x}-{3}\right)}}}={\log{{2}}}\)

Answers (1)

2020-10-20
We are given: \(\displaystyle{\log{{\left({x}+{5}\right)}}}-{\log{{\left({x}-{3}\right)}}}={\log{{2}}}\)
Use the quotient property of logarithms: \(\displaystyle{\log{{b}}}{x}-{\log{{b}}}{y}={\log{{b}}}{\left(\frac{{x}}{{y}}\right)}\) \(\displaystyle{\log{{\left(\frac{{{x}+{5}}}{{{x}-{3}}}\right)}}}={\log{{2}}}\)
Equate the arguments: \(\displaystyle\frac{{{x}+{5}}}{{{x}-{3}}}={2}\)
Multiply both sides by x=3:
x+5=2(x-3)
x+5=2x-6
-x=-11
x=11
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