Evaluate log base 9 of 27

Problem

(log_9)(27)

Solution

1. Identify the logarithmic expression and set it equal to a variable x

(log_9)(27)=x

2. Rewrite the equation in exponential form using the definition of a logarithm.

9=27

3. Express both sides of the equation using a common base, which is 3

(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=3

6. Solve for x by dividing both sides by 2

x=3/2

Final Answer

(log_9)(27)=3/2

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