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## Homework Statement

Solve:

log

_{5}(x-1) + log

_{5}(x-2) - log

_{5}(x+6) = 0

## Homework Equations

## The Attempt at a Solution

I feel like this is really simple but I cannot get the answer.

This is what I attempted

Since they have the same base, I multiplied the top

log

_{5}[(x-1)(x-2)] - log

_{5}(x+6) = 0

This gives me

log

_{5}(x

^{2}-3x+2) - log

_{5}(x+6) = 0

At this point I did not now what to do, I tried 2 methods,

1.

Since they are the same base again, I divided the top this time

log

_{5}(x

^{2}-3x+2) / (x+6) = 0

but I don't know how to continue

2.

I moved - log

_{5}(x+6) to the other side

log

_{5}(x

^{2}-3x+2) = log

_{5}(x+6)

Since they have the same base I ignored them so

x

^{2}-3x+2 = x+6

Which gave me

x

^{2}- 4x - 4

Which cannot be factored.

Please help, thankyou :)

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