How do you solve $(5^x)^(x+1)=5^(2x+12)$ ?

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Answer 1 · 2016-03-09T10:30:09

$x=-3$ or $x=4$

As $(a^m)^n=a^(mn)$ , $(5^x)^(x+1)=5^(x(x+1))=5^(x^2+x)$

Hence, $5^(x^2+x)=5^(2x+12)$ or

$x^2+x=2x+12$ or $x^2+x-2x-12=0$ or

$x^2-x-12=0$ or

$x^2-4x+3x-12=0$ or

$x(x-4)+3(x-4)=0$ or

$(x+3)(x-4)=0$ or

$x=-3$ or $x=4$

How do you solve (5^x)^(x+1)=5^(2x+12)(5^x)^(x+1)=5^(2x+12)?