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Hi :)
This is my first time using this forum, so thanks for your help in advance.
Use the laws of logs to write y as a function of x for each. Then state domain.
a) log(xy) = 2 log(x-3)
b) log(y) + 3 = log(y + 1) + log(x)
c) log (x2/y) = 2 log(x + 5)
Answers:
a) y = (x-3)2 / x
b) y = x / (1000 -x)
c) y = x2 / (x + 5)2
I got the first one by:
log(xy) = 2 log(x-3)
logx + log y = 2 log(x-3)
log y = 2 log(x-3) - logx
log y = log [ (x-3)2 / x]
I'm not sure about is how they got rid of the "log" to get only x and y in the answer, though. Are you even allowed to divide "log" and cross it out?
I don't know where they got 1000 from in b).
I started by moving all the logs that contain "y" to the left side, but I didn't know where to go from there.
And I'm not sure how to do c).
This is my first time using this forum, so thanks for your help in advance.
Homework Statement
Use the laws of logs to write y as a function of x for each. Then state domain.
a) log(xy) = 2 log(x-3)
b) log(y) + 3 = log(y + 1) + log(x)
c) log (x2/y) = 2 log(x + 5)
Answers:
a) y = (x-3)2 / x
b) y = x / (1000 -x)
c) y = x2 / (x + 5)2
The Attempt at a Solution
I got the first one by:
log(xy) = 2 log(x-3)
logx + log y = 2 log(x-3)
log y = 2 log(x-3) - logx
log y = log [ (x-3)2 / x]
I'm not sure about is how they got rid of the "log" to get only x and y in the answer, though. Are you even allowed to divide "log" and cross it out?
I don't know where they got 1000 from in b).
I started by moving all the logs that contain "y" to the left side, but I didn't know where to go from there.
And I'm not sure how to do c).