Thread: logarithms and domain, logarithm equations

1. logarithms and domain, logarithm equations

I am not sure how to work these two kinds of problems out:

1) Solve this equation:

log2 (x-3)(x+1)=5

I keep getting x= 4 or x=-2 but the solution says that the answer is -5, 7. Could someone inform me where I have made a mistake?

log2 (x-3)(x+1)=5
log2 x^2-2x-3=5
log2 x^2-2x-8=0
log2 (x-1)^2-9
log2 (x-1+3)(x-1-3)
log2 (x+2)(x-4)
x=-2, x=4

2)Find the domain of the following:

1/log2 (x^2-6x+8)

Thank you.

2. Originally Posted by jlefholtz
I am not sure how to work these two kinds of problems out:

1) Solve this equation:

log2 (x-3)(x+1)=5

I keep getting x= 4 or x=-2 but the solution says that the answer is -5, 7. Could someone inform me where I have made a mistake?

log2 (x-3)(x+1)=5
log2 x^2-2x-3=5
log2 x^2-2x-8=0
log2 (x-1)^2-9
log2 (x-1+3)(x-1-3)
log2 (x+2)(x-4)
x=-2, x=4
and you found no problem with bring the 5 over the equal sign and then putting it inside the log?

$\log_2(x - 3)(x + 1) = 5 \implies (x - 3)(x + 1) = 2^5$

2)Find the domain of the following:

1/log2 (x^2-6x+8)