Question

Evaluate the logarithmic expression without using a calculator: log_3 27.

a) 2
b) 3
c) 4
d) 5

Answer 1

To evaluate the logarithmic expression log_3 27 without a calculator, we need to find the exponent that satisfies the equation 3^x = 27. The exponent is 3, so log_3 27 = 3.

Step-by-step explanation:

To evaluate the logarithmic expression without using a calculator, we need to determine the exponent that the base needs to be raised to in order to get the argument. In this case, the base is 3 and the argument is 27. We need to find the exponent that satisfies the equation 3^x = 27.

Since 3^3 = 27, we can conclude that log_3 27 = 3.

Therefore, the correct answer is b) 3.