Evaluate log base 8 of 16

Problem

(log_8)(16)

Solution

1. Set the expression equal to a variable to represent the unknown value.

(log_8)(16)=x

2. Rewrite the logarithmic equation in exponential form using the definition by=x⇔(log_b)(x)=y

8=16

3. Express both sides with a common base by identifying that both 8 and 16 are powers of 2.

(2)x=2

4. Apply the power of a power rule (am)n=a(m*n) to simplify the left side.

2(3*x)=2

5. Equate the exponents since the bases are now identical.

3*x=4

6. Solve for x by dividing both sides by 3.

x=4/3

Final Answer

(log_8)(16)=4/3

Want more problems? Check here!