Evaluate log base 9 of 3

Problem

(log_9)(3)

Solution

1. Identify the logarithmic expression as an equation where the base 9 raised to some power x equals the argument 3

(log_9)(3)=x

2. Rewrite the logarithmic equation in exponential form.

9=3

3. Express the base 9 as a power of 3 to create a common base on both sides of the equation.

(3)x=3

4. Apply the power of a power rule to simplify the left side.

3(2*x)=3

5. Equate the exponents since the bases are now identical.

2*x=1

6. Solve for x by dividing both sides by 2

x=1/2

Final Answer

(log_9)(3)=1/2

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