Question

If log₁₀2 = a and log₁₀3 = b ; express each of the following in terms of 'a' and 'b': log 12

Answer 1

Given that log₁₀2 = a and log₁₀3 = b
log 12
= log 2 x 2 x 3
= log 2 x 2 + log 3       ...[ log_amn = log_am + log_an ]
= log 2² + log 3
= 2log 2 + log 3          ...[ nlog_am = log_amⁿ ]
= 2a + b                      ...[ ∵ log₁₀2 = a and log₁₀3 = b ]