Math
posted by Michael Weston on .
Solve
log10(8 x) − log10(1 + √x) = 2
for x.

the 10s were supposed to be subscripts so just ignore them

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. 
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