Evaluate log base 8 of 4

Problem

(log_8)(4)

Solution

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

(log_8)(4)=x

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

8=4

3. Express both sides with a common base by recognizing that both 8 and 4 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=2

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

x=2/3

Final Answer

(log_8)(4)=2/3

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