Question

logarithm chapter question 11 and no spamming plz

Answer 1

Pranam bhrata shri !!!

Here's the solution :p
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log2 (x+y) = log3 (x - y) = (log25) / (log0.2)

First let's solve (log25) / (log 0.2)

log25 /log0.2 = log 5^2 / log 5^-1

=> 2 log 5 / -1 log 5 = -2



Acc to the ques.

log 2 (x+y) = (log25) / (log0.2)

=> log 2 (x+y) = -2

=> - log 2 (x+y) = 2

=> log 2 (x+y)^-1 = 2

=> (x + y)^-1 = 4

=> x + y = 1/4 ...........1

Acc to the ques.

log3 (x - y) = (log25) / (log0.2)

=> log3 ( x-y) = -2

=> -log3 ( x-y) = 2

=> (x - y)^-1 = 3²

=> (x - y)^-1 = 9

=> x - y = 1/9...........2

Adding 1 and 2, we get

2x = 1/4 + 1/9

2x = (9+4)/36

2x = 13/36

x = 13/72

Substituting the value of x in eq 1 , we get

13/72 + y = 1/4

y = 1/4 - 13/72

y = (18 - 13)/ 72

y = 5/72

Ans. => x = 13/72 and y = 5/18.

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Hope it helps!!! :p

Thnx for the question bhrata shri :stuck_out_tongue: