Evaluate log base 4 of 512

Problem

(log_4)(512)

Solution

1. Identify the expression as a logarithm with base 4 and argument 512

2. Set the expression equal to x to create an equation.

(log_4)(512)=x

3. Rewrite the logarithmic equation in its equivalent exponential form.

4=512

4. Express both sides of the equation as powers of the same base, which is 2

(2)x=2

5. Apply the power of a power rule to simplify the left side.

2(2*x)=2

6. Equate the exponents since the bases are now equal.

2*x=9

7. Solve for x by dividing both sides by 2

x=9/2

Final Answer

(log_4)(512)=9/2

Want more problems? Check here!