Isolate the Power First

In $5\cdot {3}^{x} = 40$ the power is not alone: a 5 multiplies it. A log undoes a bare power, so first get ${3}^{x}$ by itself, exactly as you would get x by itself. Divide both sides by 5: ${3}^{x} = 8$.

Now take log base 3 of both sides: $x = \log_{3}\left(8\right)$, about 1.89. If a number is added as well, as in $4\cdot {2}^{x}+3 = 15$, undo the adding first, then the multiplying.

One trap: $5\cdot {3}^{x}$ is not ${15}^{x}$. The exponent belongs to the 3 alone, because powers come before multiplying, so the 5 and the 3 cannot be combined first.