Evaluate 3 log base 27 of 3

Problem

3*(log_27)(3)

Solution

1. Identify the logarithmic expression (log_27)(3) which represents the exponent y such that 27=3

2. Rewrite the base 27 as a power of 3 to facilitate solving for the exponent.

27=3

3. Substitute this into the exponential equation to find the value of the logarithm.

(3)y=3

4. Apply the power of a power rule (am)n=a(m*n) to simplify the left side.

3(3*y)=3

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

3*y=1

6. Solve for y by dividing both sides by 3

y=1/3

7. Multiply the result of the logarithm by the coefficient 3 from the original expression.

3⋅1/3=1

Final Answer

3*(log_27)(3)=1

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