Evaluate log base 4 of seventh root of 4

Problem

(log_4)(√(7,4))

Solution

1. Rewrite the radical expression using a fractional exponent.

√(7,4)=4^(1/7)

2. Substitute the exponential form back into the logarithmic expression.

(log_4)(4^(1/7))

3. Apply the power property of logarithms, which states (log_b)(b^x)=x

(log_4)(4^(1/7))=1/7

Final Answer

(log_4)(√(7,4))=1/7

Want more problems? Check here!