# Math

posted by .

Solve
log10(8 x) − log10(1 + √x) = 2
for x.

• Math -

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

• Math -

If the 10's are subscripts, they are meant to be the base of the log, and are important.

log10(8 x) − log10(1 + √x) = 2
log10(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 -

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

## Similar Questions

1. ### Pre Calculs

The pH of a chemical solution is given by the formula pH = -log10 [H+] where [H+] is the concentration of hydrogen ions in moles per liter. Values of pH range from 0 (acidic) to 14 (alkaline). (a) what is the pH of the solution for …
2. ### Math

How do I express these in scientific notation AND Log10 form?
3. ### math

how can you simplify this?? log10(10^.5) log10 as in log base 10 By definition: Log_10[10^(x)] = x ok, but it is 10 to the 1/2 power, not x how would you simplify it then?
4. ### phyiscs repost 2

Calculate the sound level in decibels of a sound wave that has an intensity of 2.25 µW/m2 For this question don't I use B=log10(I/IO) So it would be B=log10(2.25/1.0e-12) right?
5. ### Math

I can't calculate 1 as the answer given to the following problem. I keep getting 2. Can you show me where am I going wrong?
6. ### Algebra 2

If log10^9=0.95 and log10^2=0.30, find the following: 1. log10^9/2 2. log10^3 3. log10^36 4. log10^20/9 5. log10^900 6. log10^1/9 7. log10^1/2000 8. log10^162 I need to see all of the steps. Thanks
7. ### chemistry. am i doing this right?

1.) One of the trials in this week's experiment in chemical kinetics was determined to be 10.60 seconds. Evaluate log10(rate). log10(rate) = Would I just plug 10.60 in for the rate?
8. ### Logarithms

Using the approximation log10^2=0.301, find: log10^8
9. ### math -logarithm

Use the definition of logarithm to simplify each expression. log10 10,000 log10 10 log10 10−4
10. ### Math

What is the logarithmic function modeled by the following table?

More Similar Questions