How do I solve for x in this log equation?

[Cuisine123]

Homework Statement

0.5log(2x-1)+log\sqrt{x-9}=1

Homework Equations

N/A

The Attempt at a Solution

I have no idea how to approach this.

 

[icystrike]

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

 

[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