Evaluate log base 3 of 9

Problem

(log_3)(9)

Solution

1. Identify the base and the argument of the logarithm. The base is 3 and the argument is 9

2. Rewrite the argument 9 as a power of the base 3 Since 3×3=9 we have 9=3^2

3. Substitute the power back into the logarithmic expression to get (log_3)(3^2)

4. Apply the property of logarithms (log_b)(b^x)=x In this case, the exponent is 2

Final Answer

(log_3)(9)=2

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