Logarithms

log 24

Using the product law: log_a m + log_a n = log_a (m × n). So log 6 + log 4 = log(6 × 4) = log 24.

1

Using the quotient law: log_a m - log_a n = log_a (m/n). So log 100 - log 10 = log(100/10) = log 10 = 1 (since we're using base 10).

3

Using the power law: log_a (mⁿ) = n log_a m. So log₅ 5³ = 3 log₅ 5 = 3 × 1 = 3 (since log₅ 5 = 1).

log₅ 1, log₁₀ 1, log₂ 1

The logarithm of 1 to any base is always 0, because any number raised to the power 0 equals 1 (aº = 1). Therefore log₅ 1 = 0, log₁₀ 1 = 0, and log₂ 1 = 0. However, log₃ 3 = 1 and log₇ 7 = 1 because any number raised to power 1 equals itself.