# How do I solve 2 xx 3^x = 7 xx 5^x?

Oct 16, 2017

By arranging the equation. ($x = - 2.45$)

#### Explanation:

Divide both sides by 2 first:

${3}^{x} = 3.5 \times {5}^{x}$

Or:

${3}^{x} / {5}^{x} = 3.5$

x is approximately -2.445 (or say -2.45) (by trial and error).

${3}^{-} 2.45 = 0.0677$
${5}^{-} 2.45 = 0.0194$

that satisfy ${3}^{-} \frac{2.45}{5} ^ - 2.45 = 3.5$