How do you solve #25^(2x+3) = 125^(x-4)#?

1 Answer
AegiZz
Apr 1, 2018

#x=-9#

Explanation:

First, you have to have the same bases. This means you have to get #x^(n_1)=x^(n_2)#. After that, you can set the exponential powers equal to each other. You can simplify #25^(2x+3)# into #5^(2(2x+3))#. If you simplify that, you get #5^(4x+6)#. Using the same logic to #125^(x-4)#, you can simplify it to #5^(3(x-4))# or #5^(3x-12)#. Now, since the bases are the same, you can set #4x+6# and #3x-12# equal to each other. If you subtract #6# to the other side, and also subtracting #3x#, you get #x=-9#

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