Question #c3090

Question

1686 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-04-05T03:14:31

$x = 3$

Use the identity

$ln(a) - ln(b) -= ln(a/b)$

Therefore,

$ln(4x) - ln(x-1) = ln((4x)/(x-1))$

$= ln(6)$

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

$ln((4x)/(x-1)) = ln(6)$

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

$(4x)/(x-1) = 6$

Simplify the equation

$(4x)/(x-1) = 6$

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

$2x = 3(x-1)$

$= 3x - 3$

$0 = x - 3$

$x = 3$