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frozen [14]
3 years ago
12

Solve log81 32x - log81(x-3)=3/4 for x

Mathematics
1 answer:
MAXImum [283]3 years ago
6 0

1 step. Note that

x>0,\\ \\x-3>0\Rightarrow x>3.

Therefore, possible x are x>3.

2 step. Use property \log_ab-\log_ac=\log_a\dfrac{b}{c}.

Then

\log_{81}32x-\log_{81}(x-3)=\log_{81}\dfrac{32x}{x-3}.

3 step.

\log_{81}\dfrac{32x}{x-3}=\dfrac{3}{4}\Rightarrow 81^{\log_{81}\frac{32x}{x-3}}=81^{\frac{3}{4}},\\ \\\dfrac{32x}{x-3}=(3^4)^{\frac{3}{4}},\\ \\\dfrac{32x}{x-3}=27,\\ \\32x=27(x-3),\\ \\32x=27x-81,\\ \\5x=-81,\\ \\x=-\dfrac{81}{5}.

4 step. Since -\dfrac{81}{5} this solution is extra.

Answer: no solution, choice D.


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