Question 1179352
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The equation you show is 3^2(x+1) - 8*3^x+1 = 9 = {{{3^2(x+1) - 8*3^x+1 = 9}}}<br>
I will assume that is not the equation you wanted.<br>
If you are working problems like this, your mathematical knowledge should be sufficient to know that the proper use of parentheses is important....<br>
I will assume, to make the equation (and therefore the problem) reasonable, that this is the equation you want:<br>
3^(2(x+1)) - 8*3^(x+1) = 9 = {{{3^(2(x+1)) - 8*3^(x+1) = 9}}}<br>
Let {{{u=3^(x+1)}}}
Then note that {{{u^2 = (3^(x+1))^2 = 3^(2(x+1))}}}<br>
Then the equation is<br>
{{{u^2-8u=9}}}
{{{u^2-8u-9=0}}}
{{{(u-9)(u+1)=0}}}<br>
The two potential solutions are u=9 and u=-1.<br>
(1) u=9
{{{u = 3^(x+1) = 9 = 3^2}}}
{{{x+1=2}}}
{{{x=1}}}<br>
(2) u=-1
{{{u = 3^(x+1) = -1}}}<br>
This value of u provides no real solutions....<br>
ANSWER: there is one solution, x=1.<br>