Evaluate log base 3 of 5

Problem

(log_3)(5)

Solution

1. Identify the expression as a logarithm with base 3 and argument 5.

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

3. Use the formula (log_b)(a)=ln(a)/ln(b)

4. Substitute the values into the formula to get ln(5)/ln(3)

5. Calculate the numerical value using a calculator if a decimal approximation is required.

Final Answer

(log_3)(5)=ln(5)/ln(3)≈1.465

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