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Solve log 2...

Question

Solve ${log}_{2} (3 x - 1) - {log}_{2} (x - 2) = 3$

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Solution

${log}_{2} (3 x - 1) - {log}_{2} (x - 2) = 3$
${log}_{2} (\frac{3 x - 1}{x - 2}) = 3$ $[∵ {log}_{a} (\frac{M}{N}) = {log}_{a} M - {log}_{a} N]$
$2^{3} = \frac{3 x - 1}{x - 2}$ (exponential form)
$8 = \frac{3 x - 1}{x - 2}$
Cross multiplying, we get
$8 (x - 2) = 3 x - 1 ⟹ 8 x - 16 = 3 x - 1$
$8 x - 3 x = - 1 + 16 ⟹ 5 x = 15$
$∴ x = 3$

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