# 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 #132 : Exponential And Logarithmic Functions

Solving an exponential equation.

Solve

Explanation:

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

.

### Example Question #1 : 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 #1 : 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

### Example Question #141 : Exponential And Logarithmic Functions

Solve

.

Explanation:

After using the division rule to simplify the left hand side you can take the natural log of both sides.

If you then combine like terms you get a quadratic equation which factors to,

.

Setting each binomial equal to zero and solving for  we get the solution to be .

Solve for x:

Explanation:

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

Solve for x in the following equation:

Explanation:

### Example Question #1232 : Pre Calculus

Solve for x using the rules of logarithms:

Explanation:

Solve for x:

Explanation:

### Example Question #2 : Exponential Equations And Inequalities

Simplify the log expression: