4.4 Laws of Logarithms (3)

Question

The logarithm of a number raised to a power is the same as the 

 times the logarithm of the number. So log₄(16¹⁴) = 14 ·__________

Answer 1

There is a logarithm rule that states that log_a(bⁿ) = n * log_ab. Hence if we have log₄(16¹⁴), we know that a = 4, b = 16, and n = 14, so log₄(16¹⁴) = 14 * log₄16 by the rule. Since log₄16 = 2 because 4²=16, we know that the final answer must be 14 * 2 (which is 28).

Answer 2

log₄(16¹⁴)=14log₄16=2*14=28