How Do You Solve Exponential Inequalities Using Logarithms?

[kaspis245]

Homework Statement

$15(5^x-3^x)<16⋅15^{\frac{x}{2}}$

Homework Equations

Rules of logarithms

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?

 

[SammyS]

Homework Statement

$15(5^x-3^x)<16⋅15^{\frac{x}{2}}$

Homework Equations

Rules of logarithms

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?

I suggest dividing by 3^x .

Added in Edit:
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.