Evaluate log base 81 of 3

Problem

(log_81)(3)

Solution

1. Identify the base and the argument of the logarithm. The base is 81 and the argument is 3

2. Set up the logarithmic equation by setting the expression equal to x

(log_81)(3)=x

3. Rewrite the equation in exponential form using the definition by=x⇔(log_b)(x)=y

81=3

4. Express both sides of the equation with a common base. Since 81=3 substitute this into the equation.

(3)x=3

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

3(4*x)=3

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

4*x=1

7. Solve for x by dividing both sides by 4

x=1/4

Final Answer

(log_81)(3)=1/4

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