Evaluate log base 10 of 1.

Evaluate log base 10 of 1.

• A. 0
• B. -1
• C. 1
• D. 2

Answer: (A)

Logarithms tell us what exponent we must raise the base to in order to get the given number. For any base b that is positive and not equal to 1, log_b(1) equals 0 because b raised to the power of 0 is 1. With a base of 10, 10^0 = 1, so log base 10 of 1 is 0. If you tested other values, they’d correspond to different powers: 0.1 would come from an exponent of -1, 10 would come from an exponent of 1, and 100 from an exponent of 2. Since the number inside the log is 1, the exponent must be 0. Therefore, the value is 0.

Logarithms tell us what exponent we must raise the base to in order to get the given number. For any base b that is positive and not equal to 1, log_b(1) equals 0 because b raised to the power of 0 is 1. With a base of 10, 10^0 = 1, so log base 10 of 1 is 0.

If you tested other values, they’d correspond to different powers: 0.1 would come from an exponent of -1, 10 would come from an exponent of 1, and 100 from an exponent of 2. Since the number inside the log is 1, the exponent must be 0. Therefore, the value is 0.