Evaluate log base 16 of square root of 2

Problem

(log_16)(√(,2))

Solution

1. Rewrite the square root using a fractional exponent.

√(,2)=2(1/2)

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

16=2

3. Substitute these values into the logarithmic expression.

(log_2)(2(1/2))

4. Apply the change of base formula or the property (log_bn)(am)=m/n*(log_b)(a)

(1/2)/4*(log_2)(2)

5. Simplify the expression using the fact that (log_2)(2)=1

(1/2)/4⋅1

6. Calculate the final fraction.

1/2⋅1/4=1/8

Final Answer

(log_16)(√(,2))=1/8

Want more problems? Check here!