How do you evaluate \log _ { 7} 3+ \frac { \log _ { 7} 5} { 2} + \frac { \log _ { 7} 11} { 2}?

1 Answer
May 20, 2017

log_7 sqrt(495)

approx log_7 22.25

approx 1.59

Explanation:

Before beginning, you must know the following properties related to logarithms:-

1. a*log_cb = log_c(b^a)
2. log_ca + log_cb = log_c(a*b)

Now, in this problem,

log_7 3 + log_7 5/2 + log_7 11/2

=[2*log_7 3 + log_7 5 + log_7 11]/2

= [log_7 3^2 + log_7 (5*11)]/2

= [log_7 9 + log_7 55]/2

= [log_7 (9*55)]/2

=1/2*log_7 495

= log_7 (495^(1/2))

= log_7 sqrt(495)

approx log_7 22.25

approx 1.59