Evaluate log base 6 of cube root of 1296

Problem

(log_6)(√(3,1296))

Solution

1. Rewrite the radical expression using a fractional exponent.

√(3,1296)=1296(1/3)

2. Express the number 1296 as a power of the base 6.

1296=6

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

(6)(1/3)=6(4/3)

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

(log_6)(6(4/3))=4/3

Final Answer

(log_6)(√(3,1296))=4/3

Want more problems? Check here!