Why is the 5 in this equation, I can't multiply the 2 and 5, some of this math is so confusing
$\displaystyle 2(5)^x=7^{x+1}$
$\displaystyle 2 \cdot 5^x = 3^{x + 1} $ is equivalent to $\displaystyle \left( {\frac{5}{3}} \right)^x = \frac{3}{2}$ which has solution $\displaystyle x = \frac{{\log (3) - \log (2)}}{{\log (5) - \log (3)}}$
To see how that works divide both sides by $\displaystyle 3^x$ and also by $\displaystyle 2$.
Note that $\displaystyle \frac{{5^x }}{{3^x }} = \left( {\frac{5}{3}} \right)^x $.