How do you approximate #log_7 36# given #log_7 2=0.3562# and #log_7 3=0.5646#?

1 Answer
Oct 9, 2016

Let's first examine the prime factorization of #36#.

#36 = 6 xx 6 = 2 xx 3 xx 2 xx 3 = 2^2 xx 3^2#

So, accordingly, we can write #log_7(36)# as #log_7(2 xx 2 xx 3 xx 3)#, which by the sum rule of logarithms is equal to #log_7(2) + log_7(2) + log_7(3) + log_7(3)#.

This is equal to #0.3562 + 0.3562 + 0.5646 + 0.5646 = 1.8416#

Checking this answer using your calculator, you will find that our answer is quite close to the actual answer, #log_7(36)# having an approximate value of #1.8415644232#.

Hopefully this helps!