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

1 Answer
Shwetank Mauria
Apr 9, 2016

#x=5^5#

Explanation:

#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.

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