Evaluate log base 4 of 1/( cube root of 16)

Problem

(log_4)(1/√(3,16))

Solution

1. Rewrite the argument of the logarithm using exponents.

1/√(3,16)=1/(16(1/3))

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

16=4

3. Substitute the power back into the expression and simplify using the power of a power rule.

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

4. Apply the negative exponent rule to move the term to the numerator.

1/(4(2/3))=4(−2/3)

5. Evaluate the logarithm by applying the property (log_b)(bx)=x

(log_4)(4(−2/3))=−2/3

Final Answer

(log_4)(1/√(3,16))=−2/3

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