Evaluate log base 6 of 3

Problem

(log_6)(3)

Solution

1. Apply the change of base formula to rewrite the expression using common logarithms (base 10) or natural logarithms (base e.

(log_b)(a)=(log_c)(a)/(log_c)(b)

2. Substitute the values into the formula using natural logarithms.

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

3. Calculate the numerical values of the logarithms.

ln(3)≈1.098612

ln(6)≈1.791759

4. Divide the results to find the decimal approximation.

1.098612/1.791759≈0.613147

Final Answer

(log_6)(3)≈0.6131

Want more problems? Check here!