How do you evaluate this logarithm?

Question

log_a48 - log_a3/log_a2

 

Can you please provide working out and an explanation? 

Answer 1

Hi Widodoi,

Assuming log_a48 - log_a3 is the numerator and log_a2 is the denominator, you are missing some punctuation. Since the difference of two logs is equal to the log of a quotient, log_a48 - log_a3 can be written as log_a(48/3) or log_a16, then (log_a48 - log_a3)/log_a2 = (log_a16)/log_a2 = (log_a2⁴)/log_a2. Using the power rule log_a2⁴ = 4log_a2, so (log_a2⁴)/log_a2 = (4log_a2)/log_a2. Now divide out the common factor of log_a2 from the numerator and the denominator so that 4log_a2/log_a2 = 4