How do you solve the exponential equation #3^(x-7)=27^(2x)#?

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Answer 1 · 2017-02-19T00:29:12

#x=-7/5#

Rewrite the right hand side as follows

#3^(x-7)=(3^3)^(2x)#

Using the property #(a^y)^x=a^(yx)#

We can further rewrite the right side

#3^(x-7)=3^(6x)#

Since we now have both sides in terms of the same base

#x-7=6x#

#-5x=7#

#x=-7/5#