# Homework Help: A problem with exponents

1. Dec 14, 2015

### kaspis245

1. The problem statement, all variables and given/known data
$15(5^x-3^x)<16⋅15^{\frac{x}{2}}$

2. Relevant equations
Rules of logarithms

3. The attempt at a solution
I don't know where to start.

Here's one way to start rearranging the equation:
$5^x-3^x<16⋅15^{\frac{x-2}{2}}$

What's the correct way to start rearranging?

2. Dec 14, 2015

### SammyS

Staff Emeritus
I suggest dividing by 3x .

Then you have one term with $\displaystyle \ \left(\frac{5}{3}\right)^x \$ and another with $\displaystyle \ \left(\frac{5}{3}\right)^{x/2} \$ , the first being the square of the second.