Question

Solve without a calculator.
2ln(x+3)-ln(x-1)=3ln2
I know the answer is 1 but I dont know why

Answer 1

Convert the LHS and RHS respectively into one LN expression each.

Answer 2

That means combine everything

Answer 3

Some formulas:
\[\Large\log_na+\log_nb=\log_nab\]\[\Large\log_na-\log_nb=\log_n\frac ab\]\[\Large m\log_na=\log_na^m\]

Answer 4

but this is with ln so would it still be the same?

Answer 5

\(ln\) is just \(log\) with base \(e\)

Answer 6

oh yeah. so would \[\frac{ 2\ln(x+3) }{\ln(x+1)} = 3\ln2\] ?

Answer 7

Nope

Answer 8

then I dont understand

Answer 9

You used the formula wrongly

Answer 10

How do I use it then?

Answer 11

Use the third formula first

Answer 12

Remember that in my formulas, when you combine two things together there will be only one "ln" symbol left

Answer 13

I dont know how to do it separately but is it \[\ln\frac {x+3 }{x+1 }) ^{2}\]

Answer 14

Let's do it like this, I'll provide you all the steps, and you'll tell me if you don't understand any step

Answer 15

\[\begin{array}{rcl}
2\ln(x+3)-\ln(x-1)&=&3\ln2\\
\ln(x+3)^2-\ln(x-1)&=&\ln2^3\\
\ln\left[\frac{(x+3)^2}{x-1}\right]&=&\ln8\\
\frac{(x+3)^2}{x-1}&=&8\\
(x+3)^2&=&8(x-1)
\end{array}\]

Answer 16

ohhhhh duhh. i feel dumb now.

Answer 17

Nah, it's not your fault, it's only that I haven't explained things clearly enough.

Answer 18

its actually x+1 in my book not x-1 but still how does tht equal 1?

Answer 19

\[\begin{array}{rcl}
2\ln(x+3)-\ln(x+1)&=&3\ln2\\
\ln(x+3)^2-\ln(x+1)&=&\ln2^3\\
\ln\left[\frac{(x+3)^2}{x+1}\right]&=&\ln8\\
\frac{(x+3)^2}{x+1}&=&8\\
(x+3)^2&=&8(x+1)
\end{array}\]

Answer 20

ya i got 4 and -2 as answers tho

Answer 21

\[\begin{array}{rcl}
(x+3)^2&=&8(x+1)\\
x^2+6x+9&=&8x+8\\
x^2-2x+1&=&0\\
(x-1)^2&=&0\\
x-1&=&0\\
x&=&1
\end{array}\]

Answer 22

i obviously cant think today.

Answer 23

Well everyone got their time in a bad mood

Answer 24

want to help me with a different one?

Answer 25

Okay, post another question

Answer 26

and tag you? or u will find it?

Answer 27

Okay