Question

Use the One-to-One Property to solve the equation for x.
(Picture below)

Answer 1

what is the one to one property?
Like this?
We know that \(2^7=128 \)
So
\(2^{3x}=128 \to 2^{3x}=2^7\)
so \(3x=7\)
Hence \(x=\frac{7}{3}\)

Answer 2

x= 7/3

Answer 3

Not sure if this was the method u were looking for

Answer 4

let me get a screen shot of the one-to-one property. hold on one second.

Answer 5

ok so I used the correct method. I figured it was this. So basically the one to one method states that is the base is the same and the right hand value equals the left hand value then the exponents must equal each other

Answer 6

ohh. that makes sense. the teacher only went over one of these, we ran out of time. can you help me with this last one?

Answer 7

Ya no problem

Answer 8

Ok we need to use log properties for this one. Are u familiar with them?

Answer 9

like changing them to simplify basically? like adding, subtracting, etc?

Answer 10

Log Rules:

1) \( log_b(mn) = log_b(m) + log_b(n)\)

Answer 11

okay, yes i know those.

Answer 12

ok so \( log_3(x)+log_3(x-2)=log_3(x*(x-2))\)
So \( log_3(x)+log_3(x-2)=1 \to log_3(x*(x-2))=1\)
Can you continue from here?

Answer 13

uhh. no i can't lol. i remember doing one like this.. but not exactly.

Answer 14

ok give me a few seconds

Answer 15

okay

Answer 16

ok back

Answer 17

so \(log_3(x*(x-2))=1 \to 3^1=x*(x-2)\)
\(3=x^2-2x \to 0=x^2-2x-3\)
\(0=(x-3)(x+1)\)
Hence x=3 and -1

Answer 18

I am assuming you are familiar with quadratics and log properties but ask if you dont follow any step

Answer 19

ohh! no that makes sense! thanks so much!