# Solving for x: 3 x </msup> + 3 <mrow class="MJX-TeXAtom-ORD">

Solving for x: ${3}^{x}+{3}^{x+2}={5}^{2x-1}$
Pretty lost on this one. I tried to take the natural log of both sides but did not get the result that I desire.
I have the answer but I would like to be pointed in the right direction. Appreciated if you can give me some hints to this question, thanks!
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Sophia Mcdowell
We have
${3}^{x}+{3}^{x+2}={5}^{2x-1}\phantom{\rule{0ex}{0ex}}10\cdot {3}^{x}={5}^{2x-1}\phantom{\rule{0ex}{0ex}}50\cdot {3}^{x}={25}^{x}$
Now you can take logs

mistergoneo7
Hint:
${3}^{x}+{3}^{x+2}={3}^{x}+{3}^{x}{3}^{2}={3}^{x}+9\cdot {3}^{x}=10\cdot {3}^{x}$
$10\cdot {3}^{x}={5}^{2x-1}$
Try taking logarithms and simplifying.