Let (x0y0) be the solution of the following equations

(2x)ln2=(3y)ln3

3ln x=2ln y

Asked by Anil | 10th May, 2017, 07:53: PM

Expert Answer:

begin mathsize 16px style Consider comma space 3 to the power of lnx equals 2 to the power of lny
rightwards double arrow Taking space log space on space both space sides comma
open parentheses lnx close parentheses open parentheses ln 3 close parentheses equals open parentheses lny close parentheses open parentheses ln 2 close parentheses
rightwards double arrow lny equals fraction numerator open parentheses lnx close parentheses open parentheses ln 3 close parentheses over denominator open parentheses ln 2 close parentheses end fraction
Consider comma space open parentheses 2 straight x close parentheses to the power of ln 2 end exponent equals open parentheses 3 straight y close parentheses to the power of ln 3 end exponent
ln 2 open parentheses ln 2 plus lnx close parentheses equals ln 3 open parentheses ln 3 plus lny close parentheses
open parentheses ln 2 close parentheses squared plus ln 2 cross times lnx equals open parentheses ln 3 close parentheses squared plus ln 3 cross times lny
open parentheses ln 2 close parentheses squared plus ln 2 cross times lnx equals open parentheses ln 3 close parentheses squared plus ln 3 cross times fraction numerator open parentheses lnx close parentheses open parentheses ln 3 close parentheses over denominator open parentheses ln 2 close parentheses end fraction
rightwards double arrow negative ln 2 equals lnx
rightwards double arrow straight x equals 1 half
lny equals fraction numerator open parentheses lnx close parentheses open parentheses ln 3 close parentheses over denominator open parentheses ln 2 close parentheses end fraction equals fraction numerator begin display style 1 half end style ln 3 over denominator ln 2 end fraction equals fraction numerator ln square root of 3 over denominator ln 2 end fraction
lny equals fraction numerator ln square root of 3 over denominator ln 2 end fraction end style

Answered by Sneha shidid | 11th May, 2017, 11:03: AM