Evaluate log base 8 of 512

Problem

(log_8)(512)

Solution

1. Identify the base and the argument of the logarithm. The base is 8 and the argument is 512

2. Rewrite the expression as an equation by setting it equal to x

(log_8)(512)=x

3. Convert the logarithmic equation into its equivalent exponential form.

8=512

4. Express both sides of the equation using a common base. Since 8=2 and 512=2 substitute these values.

(2)x=2

5. Simplify the left side using the power of a power rule.

2(3*x)=2

6. Equate the exponents since the bases are the same.

3*x=9

7. Solve for x by dividing both sides by 3

x=3

Final Answer

(log_8)(512)=3

Want more problems? Check here!