What is log base 10 of 1?

What is log base 10 of 1?

• A. 0
• B. 1
• C. -1
• D. 2

Answer: (A)

Logarithms express the exponent needed to reach a number from a given base. For log base 10 of 1, you’re asking: to what exponent x must 10 be raised so that 10^x = 1? The only exponent that makes 10^x equal to 1 is x = 0, because any nonzero base raised to the 0th power is 1. So log base 10 of 1 equals 0. This aligns with the general fact that log_b(1) = 0 for any base b > 0, b ≠ 1. The other choices would give 10^1 = 10, 10^-1 = 0.1, or 10^2 = 100, not 1.

Logarithms express the exponent needed to reach a number from a given base. For log base 10 of 1, you’re asking: to what exponent x must 10 be raised so that 10^x = 1? The only exponent that makes 10^x equal to 1 is x = 0, because any nonzero base raised to the 0th power is 1. So log base 10 of 1 equals 0. This aligns with the general fact that log_b(1) = 0 for any base b > 0, b ≠ 1. The other choices would give 10^1 = 10, 10^-1 = 0.1, or 10^2 = 100, not 1.