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

1 Answer
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