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#