Evaluate log base 6 of 9

Problem

(log_6)(9)

Solution

1. Identify the expression as a logarithm with base 6 and argument 9

2. Apply the change of base formula to rewrite the expression using natural logarithms or common logarithms.

(log_b)(a)=ln(a)/ln(b)

3. Substitute the values a=9 and b=6 into the formula.

(log_6)(9)=ln(9)/ln(6)

4. Simplify the argument of the numerator by expressing 9 as 3

(log_6)(9)=ln(3)/ln(6)

5. Apply the power rule for logarithms, ln(xn)=n*ln(x) to the numerator.

(log_6)(9)=(2*ln(3))/ln(6)

Final Answer

(log_6)(9)=(2*ln(3))/ln(6)

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