Evaluate log base 6 of 17

Problem

(log_6)(17)

Solution

1. Identify the expression as a logarithm with base 6 and argument 17

2. Apply the change of base formula to rewrite the expression using natural logarithms (ln() or common logarithms ((log_10)(). The formula is (log_b)(a)=ln(a)/ln(b)

3. Substitute the values into the formula to get ln(17)/ln(6)

4. Calculate the numerical values using a calculator.

5. Evaluate the final quotient to find the decimal approximation.

Final Answer

(log_6)(17)≈1.5812

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