Evaluate log of 3 square root of 27

Problem

(log_3)(√(,27))

Solution

1. Rewrite the square root using a fractional exponent.

√(,27)=27(1/2)

2. Express the base of the power as a power of 3.

27=3

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

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

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

(log_3)(3(3/2))=3/2

Final Answer

(log_3)(√(,27))=3/2

Want more problems? Check here!