If log 2 (x+y) = log 3 (x-y)=log 25/log 0 2 find x and y - Maths - Indices and Logarithms

Question

If log 2 (x+y) = log 3 (x-y)=log 25/log 0 2 find x and y

Avinash Garg · Accepted Answer

Dear Student

we have log 2(x+y)=log 3(x-y)=log 25log 0
2take  log 2(x+y)=log 25log 0
2⇒ log 2(x+y)=log(25-0 2)⇒x+y=24 82=12
4  --(1)take log 3(x-y)=log 25log 0
2=log(25-0 2)⇒x-y=24 83=8
27----(2)add (1) and (2); we get2x=12 4+8
27⇒x=20 672=10 34from (1); 10 34+y=12 4y=12 4-10
34=2 06

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If log 2 (x+y) = log 3 (x-y)=log 25/log 0.2 find x and y