How do you solve #5^ { x + 4} = 125^ { x - 4}#?

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Answer 1 · 2017-04-25T18:43:33

#x = 8#

#5^(x+4) = 125^(x-4)#

To begin the process to solve for the variable, the base values must be the same.

#125 = 5^3#

#5^(x+4) = 5^(3(x-4))#

Now that the base is the same we can solve by setting the exponent values equal to each other.

#x+4 = 3(x-4)#

#x+4 = 3x-12#

#cancelx+4 cancel(-x) = 3x-12 -x#

#4 = 2x+12#

#4 + 12 = 2x cancel(-12) cancel(+12)#

#16 = 2x#

#16/2 = (cancel2 x)/cancel2#

#8 = x#