Question 983070


Is this the equation you need to solve?


{{{(1/8)^(2x-3)}}} = {{{16^(x+1)}}}.


If so,  then let us write it in terms of degrees of  2:


{{{2^(-3*(2x-3))}}} = {{{2^(4*(x+1))}}}.


It gives


-3*(2x-3) = 4*(x+1).


To solve the last equation,  simplify it step by step:


-6x + 9 = 4x + 4,


-6x - 4x = 4 - 9,


-10x = -5,


x = {{{(-5)/(-10)}}} = {{{1/2}}}.


<B><U>Check</U></B>. &nbsp;The left side of the original equation at &nbsp;x = {{{1/2}}}&nbsp; is &nbsp;{{{(1/8)^(1-3)}}} = {{{(1/8)^(-2)}}} = {{{8^2}}} = {{{64}}}.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The right side of the original equation at &nbsp;x = {{{1/2}}}&nbsp; is &nbsp;{{{16^(3/2)}}} = {{{4^3}}} = 64. 


<B>Answer</B>. &nbsp;x = {{{1/2}}}.