How do you solve #5^(x^2) = 25/(5^x)#?

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Answer 1 · 2017-02-03T14:18:35

#{-2, 1}#

Cross multiply:

#5^(x^2) * 5^x = 25#

Simplify using #a^n * a^m = a^(n + m)#

#5^(x^2 + x) = 25#

Write in equivalent bases.

#5^(x^2 + x) = 5^2#

#x^2 + x =2#

#x^2 + x - 2 =0#

#(x + 2)(x- 1) = 0#

#x= -2 and 1#

Hopefully this helps!