Question

log 8x - log [1+x^(1/2)] = 2
Solve for x

Answer 1

\[\log_{10}(8x) - \log_{10}(1+\sqrt{x} ) =2 \]

Answer 2

so i get \[\log_{10}\frac{ 8x }{ (1+\sqrt{x} ) } = 2\]

Answer 3

\[\Large \log(A) - \log(B) = \log(\frac{ A }{ B })\]If \[\Large \log_{10} y = k\]then\[\Large y = 10^{k}\]

Answer 4

so \[\frac{ 8x }{(1+\sqrt{x} )} = 100\]

Answer 5

Yes.

Answer 6

then i moved the denominator over to the other side and get\[8x = 100+100\sqrt{x}\]

Answer 7

Yes. Bring them all to the left. Let y = sqrt(x)

Answer 8

\[8x - 100\sqrt{x} -100\]

Answer 9

= 0.

Answer 10

\[2x - 25\sqrt{x} - 25 = 0\]

Answer 11

Let y = sqrt(x)

Answer 12

do you mean substitute y in for sqrt(x) ?

Answer 13

Yes. if y = sqrt(x) then y^2 = x

Answer 14

\[2y ^{2} - 25y - 25 = 0\]

Answer 15

Solve the quadratic equation for y. Then put back sqrt(x) in place of y and solve for x.

Answer 16

I'd need the quadratic formula right?

Answer 17

yeah.

Answer 18

I get x = 90.625 and x = -12.5

Answer 19

What are your y values?

Answer 20

y = 13.4307 and y = -.9307

Answer 21

That is what I got for y.
You square it to get x values.

Answer 22

okay so x = 180.383 and x = -.866

Answer 23

squaring makes it positive: 180.383 and 0.865
Put those back in the original equation and see if it computes to 2.

Answer 24

Got it, thank you! The 180.383 works.

Answer 25

Good. You are welcome.