Posted by Michael Weston on Sunday, November 21, 2010 at 10:33pm.
Solve
log10(8 x) − log10(1 + √x) = 2
for x.

Math  Michael Weston, Sunday, November 21, 2010 at 10:40pm
the 10s were supposed to be subscripts so just ignore them

Math  MathMate, Sunday, November 21, 2010 at 10:58pm
If the 10's are subscripts, they are meant to be the base of the log, and are important.
log_{10}(8 x) − log_{10}(1 + √x) = 2
log_{10}(8x/(1+√x)) = 2
Take antilog (or raise to power of 10)
8x/(1+√x) = 10²
8x=100(1+√x)
If you plot the graph 8x100(1+√(x)), you will find a minimum of about 400 at x=40, and a zero at about x=180.4.

Math  Reiny, Sunday, November 21, 2010 at 10:59pm
log( 8x/(1+√x) = 2
8x/(1+√x) = 100
8x = 100 + 100√x
8x  100 = 100√x
square both sides
64x^2  1600x + 10000 = 10000x
64x^2  11600x + 10 000 = 0
x = (11600 ± √132000000)/128
= 180.384 or .8662
since we squared we must check the answer
1. x = 180.384
LS = 2
RS = 2
2. x = .8662
LS = .555 ≠ RS
so x = 180.384
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