Determine if True log base 3 of 81=4

Problem

(log_3)(81)=4

Solution

1. Identify the logarithmic equation to be evaluated, which is (log_3)(81)=4

2. Rewrite the logarithmic equation in its equivalent exponential form using the definition (log_b)(x)=y⇔by=x

3. Substitute the values from the expression into the exponential form to get 3=81

4. Calculate the value of the exponential expression 3 by multiplying 3 by itself four times: 3×3×3×3=81

5. Compare the result of the calculation to the value in the equation to confirm that 81 = 81$.

Final Answer

(log_3)(81)=4* is True

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