Question

2. Express each of the following in a form free
from logarithm :
(i) 2 log x – log y = 1
(ii) 2 log x + 3 log y = log a
(iii) a log x - b log y = 2 log 3
(iv) log V= 2 log 2 - log 3 + log it + 3 log ry
(v) log F = log G+ log m, + log m2 - 2 log d​

Answer 1

$i)~2log~x - log~y=1 \\\\ 2logx - logy = log 10 \\\\ logx^2 - logy = log 10 \\\\ log x^2/y= log 10 \\\\ x^2/y= 10 \\\\ x^2= 10y\\\\\\\\ ii) 2 log x + 3 log y = log a \\\\ log x^2 + log y^3 = log a \\\\ log x^2y^3 = log a \\\\ x^2y^3= a \\\\\\\\ iii) a log x - b log y = 2 log 3 \\\\ log x^a - logy^b = log3^2 \\\\ log x^a/y^b = log 3^2 \\\\ x^a/y^a = 9\\\\\\\\ iv) I ~didn't~ get~ it~ \\\\\\\\v)log F = log G+ log m, + log m2 - 2 log d \\\\ log F= log Gmm2 - log d^2 \\\\ log F= log Gmm2/ d^2 \\\\ F = \frac{Gmm_2}{d^2}$

All questions can be simplified in similar way if you know the laws of logarithms