$3^{2x}-2\left(3^x\right)=3$
My solution:
$\left(3^x\right)^2-2\cdot \:3^x=3$
Make the substitution $3^x=u$
$\left(u\right)^2-2u=3$
$u^2-2u-3=0$
$u=3,\:u=-1$
No solution for $3^x=-1$
$3^x=3$
I was wondering how i can do this question using logarithms?
then $x=1$
Best Answer
To answer your specific inquiry:
I guess your asking if a solution would exist by taking the log of both sides. If this is what you mean, then I would say it is is possible but is not simple. Your solution is better. The expression:
$log(x-y) = log (z)$
Is not an expression you can manipulate further with ease.
Remember that:
$(log(x-y))$ is NOT always equal to ($log (x) - log (y))$
In fact, the equality only holds for specific values of y and x:
As a result, since you can't simplify the original problem by taking the log of both sides, your answer is good.