Evaluate log base 9 of 7

Problem

(log_9)(7)

Solution

1. Identify the expression as a logarithm with base 9 and argument 7

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

3. Substitute the values into the formula to get ln(7)/ln(9)

4. Simplify the denominator if possible by noting that 9=3 which allows the expression to be written as ln(7)/(2*ln(3))

5. Calculate the numerical value using a calculator for a decimal approximation.

Final Answer

(log_9)(7)=ln(7)/ln(9)≈0.8856

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