How do you solve $log_5 x^3=15$ ?

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Answer 1 · 2016-04-09T05:24:13

$x=5^5$

$log_5x^3=15$ means $5^15=x^3$

As $(5^5)^3=5^15$

$x^3=(5^5)^3$ i.e. $x^3-(5^5)^3=0$ , which can be factorized as

$(x-5^5)(x^2+5^5x+(5^5)^2)=0$

i.e. $x=5^5$ , if we consider the domain only as real numbers.

as $x^2+5^5x+(5^5)^2$ is of the type $x^2+ax+a^2$ and has complex roots because discriminant, which is $a^2-4a^2=-3a^2$ , is always negative.

How do you solve log_5 x^3=15log_5 x^3=15?