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 anti-log (or raise to power of 10)

8x/(1+√x) = 10²

8x=100(1+√x)

If you plot the graph 8x-100(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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