SOLUTION: solve for y in logy10+log10y=5

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Question 534129: solve for y in logy10+log10y=5
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Change of variable.
Let x be defined as
x=log%2810%2Cy%29 so that later we'll use y=10%5Ex
log%28y%2C10%29=1%2Flog%2810%2Cy%29, so
log%28y%2C10%29=1%2Fx
The equation on x is
x%2B1%2Fx=5
Which transforms into
x%5E2-5x%2B1=0
x+=+%285+%2B-+sqrt%28+21+%29%29%2F2+ and y=10%5Ex
which I cannot make look pretty

x=100sqrt%2810%2A10%5Esqrt%2821%29%29 and
x=100sqrt%2810%2A10%5E%28-sqrt%2821%29%29%29=100sqrt%2810%2F10%5Esqrt%2821%29%29
Approximate values are
61842.62 and 1.617008