# Precalculus : Use Logarithms To Solve Exponential Equations and Inequalities

## Example Questions

### Example Question #1 : Use Logarithms To Solve Exponential Equations And Inequalities

Solving an exponential equation.

Solve for ,

.

Explanation:

We recall the property:

Now, .

Thus

.

### Example Question #2 : Use Logarithms To Solve Exponential Equations And Inequalities

Solving an exponential equation.

Solve

Explanation:

Use  (which is just , by convention) to solve.

.

### Example Question #3 : Use Logarithms To Solve Exponential Equations And Inequalities

Solve the equation for  using the rules of logarithms.

Explanation:

Expanding the logarithms into sums of logarithms will cancel out the first two x terms, resulting in the equation:

Combining the first and second terms, then subtracting the new term over will allow you to isolate the variable term.

Divide both sides of the equation by 2, then exponentiate with 3.

Evaluating this term numerically will give the correct answer.

### Example Question #4 : Use Logarithms To Solve Exponential Equations And Inequalities

Solve the following equation:

Explanation:

To solve this equation, recall the following property:

Can be rewritten as

Evaluate with your calculator to get

Solve

.