High School Math : Logarithms

Example Questions

Example Question #3 : Simplifying Logarithms

Which of the following expressions is equivalent to

Explanation:

According to the rule for exponents of logarithms,. As a direct application of this,.

Example Question #4 : Simplifying Logarithms

Simplify the expression below.

Explanation:

Based on the definition of exponents, .

Then, we use the following rule of logarithms:

Thus,

Example Question #1 : Solving Logarithmic Equations

Solve the equation.

Explanation:

Change 81 to  so that both sides have the same base. Once you have the same base, apply log to both sides so that you can set the exponential expressions equal to each other (). Thus, .

Example Question #2 : Solving Logarithmic Equations

Solve the equation.

Explanation:

Change the left side to  and the right side to  so that both sides have the same base. Apply log to both sides and then set the exponential expressions equal to each other (). .

Example Question #3 : Solving Logarithmic Equations

Solve the equation.

Explanation:

Change the left side to  and the right side to  so that both sides have the same base. Apply log and then set the exponential expressions equal to each other (). Thus, .

Example Question #4 : Solving Logarithmic Equations

Solve the equation.

Explanation:

Change the left side to  and the right side to  so that both sides have the same base. Apply log and then set the exponential expressions equal to each other (). Thus,

Example Question #5 : Solving Logarithmic Equations

Solve the equation.

Explanation:

Change the left side to  and the right side to  so that both sides have the same base. Apply log to both sides and then set the exponential expressions equal to each other (). Thus, .

Example Question #6 : Solving Logarithmic Equations

Solve for .

Explanation:

can be simplified to  since . This gives the equation:

Subtracting  from both sides of the equation gives the value for .

Example Question #7 : Solving Logarithmic Equations

Solve the equation.

Explanation:

First, change 25 to  so that both sides have the same base. Once they have the same base, you can apply log to both sides so that you can set their exponents equal to each other, which yields .

Example Question #8 : Solving Logarithmic Equations

Solve the equation.