How do you solve $25^(x-4)=5^(3x+1)$ ?

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Answer 1 · 2016-06-20T17:35:34

$color(blue)(x=-9$

$25 ^ ( x-4) = 5 ^ (3x +1)$

$25$ can also be expressed as $25 = 5^2$

So, $25 ^ ( x-4)$ can be expressed as $5 ^ (2 * (x -4)) = color(blue)(5^ (2x - 8)$

Now, our expression becomes:

$color(blue)(5^ (2x - 8) )= 5 ^ (3x +1)$

As we can observe here, the bases are equal, so we equate the powers to each other and obtain $x.$

$2x - 8 = 3x+1$

$- 8 -1 = 3x-2x$

$- 9 = x$

$color(blue)(x=-9$

How do you solve 25^(x-4)=5^(3x+1)25^(x-4)=5^(3x+1)?