Question

log base x(5x - 6) = 2.​

Answer 1

We have,

$log_{x}(5x - 6) = 2$

Using base change property,

$\frac{ log(5x - 6) }{ log(x) } = 2 \\ \\ log(5x - 6) = 2 log(x) \\ \\ log(5x - 6) = log( {x}^{2} ) \\ \\ 5x - 6 = {x}^{2} \\ \\ {x}^{2} - 5x + 6 = 0 \\ \\ {x}^{2} - 3x - 2 x + 6 = 0 \\ \\ x(x - 3) - 2(x - 3) = 0 \\ \\ (x - 3)(x - 2) = 0$

Therefore we have values of x as 3 as well as 2.