Logarithm Calculation: Find the Exact Value of log8(4)

Understanding Logarithms

The expression log8(4) represents the logarithm of 4 to the base 8. In simpler terms, it asks: 'To what power must we raise 8 to get 4?'

Solving the Expression

1. Equation: We need to solve the equation 8^x = 4, where x is the unknown exponent.

2. Expressing 4 as a Power of 8: We can rewrite 4 as 8^(1/2) since 8^(1/2) = √8 = 2.

3. Equating Exponents: Our equation becomes 8^x = 8^(1/2). Since the bases are the same, the exponents must be equal.

4. Solution: Therefore, x = 1/2.

Conclusion

The exact value of the expression log8(4) is 1/2.