Question

help pleaseeeeeeeeeeeeeeeee =(

Answer 1

With What.?

Answer 2

\[8^{n+1}+8^{n}=36 \] n=

Answer 3

i got 5/2

Answer 4

Thats Correct

Answer 5

it's supposed to be 2/3 tho...

Answer 6

What did you do?

Answer 7

i did the exponents like this 3n+3+3n=18

Answer 8

\(8^{n+1}\) is same as \(8\cdot8^n\), right?

So you have \(8^{n+1}+8^n = 8\cdot8^{n}+8^n\)

Now you can factor \(8^n\) out.

Answer 9

so was my answer wrong?

Answer 10

yeah n is not 5/2.

Answer 11

oh so u cant do anything if the base is the same and even if they have exponents if they're addition of subtraction sign? It has to be multiplication to do anything? like adding exponents and such?

Answer 12

or subtraction not of*

Answer 13

yeah, for you to add exponent and stuffs, you need to have base multiplied; \(a^ba^c = a^{b+c}\)

But here, you have \(8^{n+1}+8^n\). You have plus sign instead.

Answer 14

But you can factor it out; you just need exponent to be same

Answer 15

so whats the next step?

Answer 16

Like I said, \(8^{n+1}\) is same as \(8\cdot8^n\), right?

So you have \(8^{n+1}+8^n = 8\cdot8^{n}+8^n\)

Now you can factor \(8^n\) out.

Answer 17

Factoring \(8^n\) out will get you \(8^n~(8+1)\)

Answer 18

wait sorry where does the +1 come from

Answer 19

\(8^{n+1}+8^n = 8\cdot8^{n}+\color{red}{1}\cdot8^n = 8^n~(8+\color{red}{1})\)

Answer 20

\(8^n\) is same as \(1\cdot8^n\)

Answer 21

Does that make sense?

Answer 22

ummm kind of.....so basically the one is fo the 8^n right?

Answer 23

yeah.

Answer 24

okay i mean it's kind of weird but maybe i have to keep looking at it for it to sink in

Answer 25

It's just like \(ba+a~~\Rightarrow~~a~(b+1)\)

Answer 26

oh okay i got it
thanks

Answer 27

Ok so you have: \[8^n(8+1)=36\]\[8^n(9)=36\] Divide both sides by 9:
\[8^n=4\]

Now convert base to 2;
\[(2^3)^n = 2^2\]\[2^{3n} = 2^2\]

Then since bases are same, we can set exponents equal to each other; \[3n = 2\]\[\boxed{n=\dfrac{2}{3}}\]

Answer 28

Make sense so far?

Answer 29

yea i was just having trouble with the factoring i got it now thank you so much youre awesome!!!!!

Answer 30

ok you are welcome :)