Question

Ln(X+1)^2=2
Please solve and explain how. I will medal.

Answer 1

Is the Ln the natural log?

Answer 2

properties of logs:

so,
2ln(x+1) = 2
ln(x+1) = 1
e = x + 1
x = e-1

Answer 3

^ Exactly what Gralwyn said :P

Answer 4

@Gralwyn The way I'm interpreting it, \(\ln(x+1)^2\neq2\ln(x+1)\). The log is squared, and not the \(x+1\).

Answer 5

@KingGeorge Then it would be written as (ln(x+1))^2

Answer 6

\[(\ln(x+1))^2\]

Answer 7

I can't distinguish between either in this case. Do you know which one it is @Bigjoe11?

Answer 8

But the way it is written, it doesn't have those parantheses, so it can't be the whole log squared.

Answer 9

Even if it wasn't, properties of logs would still allow the 2 to be moved to the front. And like Gralwyn said, the whole quantity including the log would have to be squared

Answer 10

@dixiemitsy are you sure about that?

Answer 11

The properties of logs would not allow the 2 to be moved in front. If the whole log were squared, this would actually become a rather difficult question. In retrospect, you are probably correct Gralwyn. But ordinarily, I would interpret the logarithm being squared.

Answer 12

In fact, if you type the problem into wolfram as is, wolfram will interpret it as the logarithm being squared.

Answer 13

Lets say that the whole log were squared, then the answer would be:

ln(x+1) = sqrt(2)
e^(sqrt(2)) = x+1

e^(sqrt(2)) - 1 = x

e^(2^(1/2)) - 1 = x
e - 1 = x

what?

Answer 14

i probably did something dumb when i multiplied the 2 and 1/2 since e^(sqrt(2)) isn't equal to e^1

Answer 15

Still never understood why I can't do that

Answer 16

The 2 and power of 1/2 don't quite cancel like that. But other than that it looks mostly fine. You would get a second solution of \(x=e^{-\sqrt2}-1\) as well though.

Answer 17

So depending on what the exact question is, the solution should either be\[x=e-1\]or\[x=e^{\sqrt2}-1,\quad x=e^{-\sqrt2}-1\]

Answer 18

actually when you write ln(x+1)^2, this actually means [ln(x+1)]^2.

If you want (x+1) to be squared, you must be specific and write ln[(x+1)^2]

Answer 19

the same convention holds for sin(x)^2 = sin^2(x) = (sinx)^2

Answer 20

Of course, not all people follow this convention. This why it is always better to use parentheses. Plus calculators are also programmed to follow this convention.

Answer 21

Exactly my thoughts. Well said.

Answer 22

so if you type ln(2)^2, your calculator will compute (ln(2))^2

Answer 23

Thanks for the help guys! It helped a ton!