Evaluate log base 27 of 9

Problem

(log_27)(9)

Solution

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

(log_27)(9)=x

2. Rewrite the logarithmic equation in its equivalent exponential form.

27=9

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

(3)x=3

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

3(3*x)=3

5. Equate the exponents since the bases are the same.

3*x=2

6. Solve for x by dividing both sides by 3

x=2/3

Final Answer

(log_27)(9)=2/3

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