Evaluate log base 3 of 4

Problem

(log_3)(4)

Solution

1. Apply the change of base formula to rewrite the logarithm in terms of natural logarithms or common logarithms.

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

2. Substitute the values a=4 and b=3 into the formula.

(log_3)(4)=ln(4)/ln(3)

3. Simplify the numerator if possible by expressing 4 as 2 and using the power rule for logarithms.

ln(4)=ln(2)=2*ln(2)

4. Combine the results to find the exact value.

(log_3)(4)=(2*ln(2))/ln(3)

Final Answer

(log_3)(4)=ln(4)/ln(3)

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