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#