Evaluate log base 18 of 2.3

Problem

(log_18)(2.3)

Solution

1. Identify the expression as a logarithm with a non-standard base, specifically base 18 and argument 2.3

2. Apply the change of base formula to convert the expression into a form that can be calculated using common logarithms (base 10 or natural logarithms (base e.

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

4. Substitute the given values into the formula: ln(2.3)/ln(18)

5. Calculate the numerical values of the natural logarithms: ln(2.3)≈0.832909 and ln(18)≈2.890372

6. Divide the results to find the final decimal approximation: 0.832909/2.890372≈0.288167

Final Answer

(log_18)(2.3)≈0.288167

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