How Do You Solve Exponential Inequalities Using Logarithms?

  • Thread starter kaspis245
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  • #1
kaspis245
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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?
 
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  • #2
kaspis245 said:

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 3x .

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.
 
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