# Math Help - Limit involving a constant to the x

1. ## Limit involving a constant to the x

I need some help with this:

lim x->0 of ( (3^2x) - 1 ) / ( (3^x) - 1)

The answer should be 2, but I keep getting 0.

I multiply the top and bottom by ( (3^x) + 1) and get this:

((3^3x) + (3^2x) - (3^x) -1) / ((3^2x) + (3^x) - (3^x) - 1)

And so that gives me 0/0.

2. Originally Posted by nautica17
I need some help with this:

lim x->0 of ( (3^2x) - 1 ) / ( (3^x) - 1)

The answer should be 2, but I keep getting 0.

I multiply the top and bottom by ( (3^x) + 1) and get this:

((3^3x) + (3^2x) - (3^x) -1) / ((3^2x) + (3^x) - (3^x) - 1)

And so that gives me 0/0.

Just think about it like this $3^{2x}-1=\left(3^x\right)^2-1=\left(3^x-1\right)\left(3^x+1\right)$
Just think about it like this $3^{2x}-1=\left(3^x\right)^2-1=\left(3^x-1\right)\left(3^x+1\right)$