Question

Answer the following:

Show that `7log (15/16) + 6log(8/3) + 5log (2/5) + log(32/25)` = log 3

Answer 1

L.H.S. = `7log (15/16) + 6log(8/3) + 5log (2/5) + log(32/25)`

= `log(15/16)^7 + log(8/3)^6 + log(2/5)^5 + log(32/25)`

= `log((3 xx 5)/2^4)^7 + log(2^3/3)^6 + log(2/5)^5 + log(2^5/5^2)`

= `log((3^7 xx 5^7)/2^28) + log(2^18/3^6) + log(2^5/5^5) + log(2^5/5^2)`

= `log[(3^7 xx 5^7)/2^28 xx 2^18/3^6 xx 2^5/5^5 xx 2^5/5^2]`

= log 3

= R.H.S.