Question #c3090

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Question #c3090

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Answer 1 · 2016-04-05T03:14:31

$x = 3$ $x = 3$

Explanation:

Use the identity

$ln (a) - ln (b) \equiv ln (\frac{a}{b})$ $ln(a) - ln(b) -= ln(a/b)$

Therefore,

$ln (4 x) - ln (x - 1) = ln (\frac{4 x}{x - 1})$ $ln(4x) - ln(x-1) = ln((4x)/(x-1))$

$= ln (6)$ $= ln(6)$

Since $ln$ $ln$ is an inverse function, we take the exponential with base $e$ $e$ on both sides to "undo" the $ln$ $ln$ .

$ln (\frac{4 x}{x - 1}) = ln (6)$ $ln((4x)/(x-1)) = ln(6)$

$e^{ln (\frac{4 x}{x - 1})} = e^{ln (6)}$ $e^{ln((4x)/(x-1))} = e^{ln(6)}$

$\frac{4 x}{x - 1} = 6$ $(4x)/(x-1) = 6$

Simplify the equation

$\frac{4 x}{x - 1} = 6$ $(4x)/(x-1) = 6$

$\frac{2 x}{x - 1} = 3$ $(2x)/(x-1) = 3$

$2 x = 3 (x - 1)$ $2x = 3(x-1)$

$= 3 x - 3$ $= 3x - 3$

$0 = x - 3$ $0 = x - 3$

$x = 3$ $x = 3$

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Question #c3090

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