Evaluate log base 2 of ( square root of 2)^5

Problem

(log_2)(√(,2))

Solution

1. Rewrite the square root using a fractional exponent.

√(,2)=2(1/2)

2. Apply the power of a power rule for exponents to simplify the expression inside the logarithm.

(2(1/2))5=2(5/2)

3. Substitute the simplified expression back into the logarithm.

(log_2)(2(5/2))

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

(log_2)(2(5/2))=5/2

Final Answer

(log_2)(√(,2))=5/2

Want more problems? Check here!