141st Problem 2017

Solution 1:

$3^x=9^{x+3}$

$3^x=3^{2(x+3)}$

$x=2x+6$

$x=-6$ $\boxed{\color{#624F41}\large answer}$

Solution 2.

Take the natural logarithm of both sides.

$\ln3^x=\ln9^{x+3}$

$x~\ln3=(x+3)~\ln9$

$x=\dfrac{(x+3)~\ln9}{\ln3}$

$x=2(x+3)$

$x=-6$ $\boxed{\color{#624F41}\large answer}$

$\displaystyle 3^x = 9^{x \ + \ 3}$

$\displaystyle 3^x = (3^2)^{x \ + \ 3}$

$\displaystyle 3^x = 3^{2(x \ + \ 3)}$

$\displaystyle x = 2x + 6$

$\displaystyle x = - 6$