# Homework Help: Solving Exponential Equations

1. Jan 26, 2012

### anonymous12

1. The problem statement, all variables and given/known data
Solve $2^{k-2}=3^{k+1}$

2. Relevant equations

3. The attempt at a solution
$$2^{k-2}=3^{k+1}$$
$$\frac{2^{k}}{2^{2}}=(3^k)(3^1)$$
$$\frac{2^{k}}{3^{k}} = 4 \cdot 3$$
$$\frac{2^{k}}{3^{k}} = 12$$

What do I do next to solve for K?

2. Jan 26, 2012

### Mentallic

Use the fact that $$\frac{a^n}{b^n}=\left(\frac{a}{b}\right)^n$$ and also, what do you know about logarithms?

3. Jan 27, 2012

### HallsofIvy

You could have used logarithms right from the start- $log(2^{k-2})= log(3^{k+1})$.

In general, to solve an equation of the form f(x)= constant or f(p(x))= f(q(x)) you will need to use the inverse function to f. And the inverse of the exponential is the logarithm.

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