How do you solve the exponential equation #5^(3x)=25^(x-4)#?

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Answer 1 · 2017-08-24T06:23:34

#x=-8#

As a first approach to solving exponential equations, try to either:

In this case, notice that #25# is a power of #5," "color(blue)(25 =5^2)#

#5^(3x) = color(blue)(25)^(x-4)#

#5^(3x) = color(blue)((5^2))^(x-4)" "larr# multiply the indices

#color(red)(5)^(3x) = color(red)(5)^(2x-8)" "larr# the bases are the same

#:. 3x = 2x-8" "larr# the indices are equal

#3x -2x =-8#

#x=-8#