SOLUTION: sovle simultaneously xy=160 logx-3logy=1

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Question 1106541: sovle simultaneously
xy=160
logx-3logy=1
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
sub for y,

log%28%28x%29%29-log%28%28%28160%2Fx%29%5E3%29%29=1
.
.
log%28%28%28x%5E4%2F160%5E3%29%29%29=1
.
.
log%28%28x%29%29=%281%2B3%2Alog%28%28160%29%29%29%2F4
log%28%28x%29%29=1.90309
highlight%28x=80%29

Returning to xy=160, highlight%28y=2%29.

Answer by greenestamps(13215) About Me  (Show Source):
You can put this solution on YOUR website!


log%28x%29-3log%28y%29+=+1
log%28x%2Fy%5E3%29+=+log%2810%29
x%2Fy%5E3+=+10
x+=+10y%5E3
xy+=+10y%5E4+=+160
y%5E4+=+16
y+=+2

We need to choose the positive 4th root of 16, because the log of a negative number is undefined.

y = 2; x = 80