I'm going through logarithms at the moment, and I can't solve this simultaneous equation: logx−log2=2logy x−5y+2=0 I've tried substituting both x and y to no avail: log((5y−2)/2)=logy^2 or: log(x/2)=log((x+2)/5)^2 But I can't get passed that. Can someone point out what direction I need to go in?

Pierre Holmes

Pierre Holmes

Answered question

2022-07-15

Simultaneous log equations
I'm going through logarithms at the moment, and I can't solve this simultaneous equation:
log x log 2 = 2 log y
x 5 y + 2 = 0
I've tried substituting both x and y to no avail:
log ( 5 y 2 2 ) = log y 2
or:
log ( x 2 ) = log ( x + 2 5 ) 2
But I can't get passed that. Can someone point out what direction I need to go in?

Answer & Explanation

Abraham Norris

Abraham Norris

Beginner2022-07-16Added 16 answers

From the first equation we get x 2 = y 2 so with the second equation we get
2 y 2 5 y + 2 = 0 , y > 0
can you take it from here?
Kyle Liu

Kyle Liu

Beginner2022-07-17Added 4 answers

From
log ( x 2 ) = log ( x + 2 5 ) 2
you can raise to the power 10 on both sides and get
x 2 = ( x + 2 5 ) 2 .

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