# Homework Help: How do I solve for x in this log equation?

1. Jan 4, 2010

### Cuisine123

1. The problem statement, all variables and given/known data
0.5log(2x-1)+log$$\sqrt{x-9}$$=1

2. Relevant equations
N/A

3. The attempt at a solution
I have no idea how to approach this.

2. Jan 4, 2010

### icystrike

use this laws:
alogb=$$logb^{a}$$
logm+logn=logmn

3. Jan 4, 2010

### TauCrouton

first, rewrite the square root as an exponent, and rewrite 1 as log(10), so you get

0.5log(2x-1) + log(x-9)^(1/2) = log(10)

Bring the exponent down to get 0.5log(x-9)

0.5log(2x-1) + 0.5log(x-9) = log(10)

multiply both sides by 2

log(2x-1) + log(x-9) = 2log(10)

Raise the 10 in the log function to the 2 (100) and multiply the two inner log functions

log[(2x-1)(x-9)] = log(100)

take the antilog of both sides and solve for x

(2x-1)(x-9) = 100

2x^2 - 19x - 91

X=13
X= -3.5