I need to solve the exponential equation $((x + 4)10^x)/(x - 3) = 2x(10^x)$ assuming the fact that $2^x$ is always positive.
The example uses the case $x^3-2^x - 3(2^x) = 0$ factors out $2^x$ leaving $2^x (x^3-3) = 0$. They then apply the zero-product property and solve $2^x$ and $x^3 - 3 = 0$. Does this still apply for my more complex question? In that case, would I get one side of the equation to $0$, then apply this same property? Thanks in advance for any assistance.