Evaluate log base 4 of 134

Problem

(log_4)(134)

Solution

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

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

2. Substitute the given values into the formula.

(log_4)(134)=ln(134)/ln(4)

3. Calculate the values of the natural logarithms.

ln(134)≈4.8978398

ln(4)≈1.3862944

4. Divide the results to find the final decimal value.

4.8978398/1.3862944≈3.5330445

Final Answer

(log_4)(134)≈3.5330445

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