Question

Answer the following:

Find value of `(3 + log_10 343)/(2 + 1/2 log_10 (49/4) + 1/2 log_10 (1/25)`

Answer 1

`(3 + log_10 343)/(2 + 1/2 log_10 (49/4) + 1/2 log_10 (1/25)`

= `(3 + log_10 7^3)/(2 + log_10 (49/4)^(1/2) + log_10 (1/25)^(1/2)`

= `(3 + 3.log_10 7)/(2 + log_10  7/2 + log_10  1/5)`

= `(3(1 + log_10 7))/(2 + log_10 (7/2 xx 1/5)`

= `(3(1 + log_10 7))/(2 + log_10 (7/10))`

= `(3(1 + log_10 7))/(2 + log_10 7 - log_10 10)`

= `(3(1 + log_10 7))/(2 + log_10 7 - 1)`   ...[∵ log_a a = 1]

= `(3(1 + log_10 7))/(1 + log_10 7)`

= 3