College Algebra: Logarithms, please help! (-.-)
Solve for x: (look in comments)

Question

College Algebra: Logarithms, please help! (-.-)
Solve for x: (look in comments)

anonymous · Answer

$$\log _{7}(3x-9)-\log _{7}(2x-6)=0$$

ganeshie8 · Answer

is the right hand side really 0 ?

anonymous · Answer

Yes, that's how it looks in my study packet.

anonymous · Answer

The packet gave me 4 answer choices:
a.) 3
b.) all real numbers
c.) -3
d.) no solution

ganeshie8 · Answer

Okay send that negative log to right side and remove the log both sides

ganeshie8 · Answer

$$\log _{7}(3x-9) = \log _{7}(2x-6)$$

$$3x-9 = 2x-6$$

solve $x$

anonymous · Answer

See, I thought the answer was 3 as well, but the answer is suppose to be D. I don't know why that is the answer...

ganeshie8 · Answer

you get $x=3$ by solving but it could be an extraneous solution, so you need to plug that back intot he original equation and verify if it really works

anonymous · Answer

Ohhh. I have a bad habit of not plugging the answer back into the equation. I'll try that now.

ganeshie8 · Answer

Keep in mind $\log(x)$ as a real valued function is defined only for  $x\gt 0$

anonymous · Answer

I will, thank you very much!!