Evaluate log base 4 of cube root of 16

Problem

(log_4)(√(3,16))

Solution

1. Rewrite the cube root using a fractional exponent.

√(3,16)=16(1/3)

2. Express the base of the power, 16, as a power of 4.

16=4

3. Substitute this back into the expression and apply the power of a power rule.

(4)(1/3)=4(2/3)

4. Apply the logarithm property (log_b)(bx)=x to evaluate the expression.

(log_4)(4(2/3))=2/3

Final Answer

(log_4)(√(3,16))=2/3

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