SOLUTION: I have an exponential equation - not sure if I went about it in the right way or not... (125/8)^x+1 = (2/5)^x-1 for want of a better way of doing things I decided to ma

Question 160268: I have an exponential equation - not sure if I went about it in the right way or not...
(125/8)^x+1 = (2/5)^x-1

for want of a better way of doing things I decided to make both values inside the parentheses to be divided by the same thing thus
(625/40)^x+1 = (16/40)^x-1
then decided to combine to get the exponentials from x+1 - (x-1) to = 2
and then combining the other to give me a final answer of (609/40)^2
Is this correct or how else should I do this please?
Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!




Notice that  and that  so 
so replace  by :



Multiply exponents on the left:



Distribute: 



Now observe that on the right the base  is the 
reciprocal of the base on the left, and the reciprocal
is the  power, so write  on the right as :



Multiply the exponents on the right:



Distribute:



Since both sides are powers of the same base, and
since that base is neither 0 nor 1, we may equate
the exponents and drop the bases:









Edwin

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