Use Logarithms To Solve Exponential Equations and Inequalities - Pre-Calculus

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

.

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 .

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.

To solve this equation, recall the following property:

Can be rewritten as

Evaluate with your calculator to get

The logarithmic expression is as simplified as can be.

The logarithmic expression is as simplified as can be.

We recall the property:

Now, .

Thus

.

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

.

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 .

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.

To solve this equation, recall the following property:

Can be rewritten as

Evaluate with your calculator to get