If 3^n+2 = 81, what does n equal?

Question

N=2

how do i get this?

Answer 1

3^(n + 2) = 81
n + 2 = 4
n = 2

PS
Use brackets to clarify question.
What you have in fact typed means:-
(3^n) + 2 = 81
i.e. a completely different question.

Answer 2

Hello,
3^(n+2) = 81 so 3^(n+2) = 3^4 so since the bases the exponents must be equal then n+2 = 4 so n = 2.

Hope This Helps!

Answer 3

n = 2

4th root of 81 = 3

3^4 = 81

Answer 4

3^(n+2)=81 dont get confuse with 3^n+2=81

Your answer suggest we have 3^(n+2)=81 situation.

so it means 3 times how many it self will be 81?
3 = 3
3*3=9
3*3*3=27
3*3*3*3=81

Now you get 3^4 = 81
4=n+2
n=2

Answer 5

oh, you mean 3^(n+2)=81 xD
To do this, you'll need to know some logarithm laws:
Log2(2^x)=x
Log3(3^x)=x
Log base 'x', x to the power of something always equals something
Sooo, you could do:
Log3(3^n+2)=Log3(81)
n+2=4
n=2

Another law is that Log(x)^y=yLog(x)
Sooo, you could also do Log(3^(n+2))=log(81)
(n+2)(Log(3))=Log(81)
N+2=Log(81)/Log(3)
n=(Log(81)/Log(3))-2
n=2

The last way is to just think of exponentials
3^(n+2)=81, 81=3^4
3^(n+2)=3^4, get rid of the bases, since they are the same
n+2=4
n=2

Answer 6

I assume you meant

3^(n+2)=81 not 3^n +2 =81

3^(n+2) = 3^n (3^2) =81
3^n = 9

3^2 =9 , hence n =2

To avoid any confusion, please use parentheses to make it easy for all

Answer 7

n does not equal 2
3^2 +2= 11

get to 3^n=79
now do ln3^n=ln79
ln is the natural log on calculator
n=ln79/ln3
n=3.977242834

Answer 8

3^n+2 = 81
3^n = 79
ln(3^n) = ln(79)
(n)ln(3) = ln(79)
n = ln(79)/ln(3)

or is it 3^(n+2)?
if this is the case, you know that 3^4 = 81. so if you set up the equation like this:
n+2 = 4
n=2.

Answer 9

3x3=9x3=27x3=81
this is 3^4
s0 n=2