2 Answers

Nitramk · Answer 1 · 2019-10-27T23:31:53+0000

Combine the left hand side, then write both sides as powers of 6:

$\log_64x^2-\log_6x=\log_6\frac{4x^2}x=2\implies6^{\log_6\frac{4x^2}x}=6^2$

$\implies\frac{4x^2}x=36$

$\implies x^2=9x$

$\implies x^2-9x=x(x-9)=0$

$\implies x=0,x=9$

However, for any base
,
$\log_bx$ is undefined if
x=0 , so the only solution is
x=9 .

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