# Solve for n `3^(n-2) = 27`

Asked on by nick-teal

### 8 Answers

vamkitten | Student, Undergraduate | (Level 1) Honors

Posted on

3^n-2=27

3^n-2=3^3

n-2=3

n=5

swaathi787 | eNotes Newbie

Posted on

27 on the right hand side can be written as 3^3 thereby allowing the same base (3) to be present on both sides. Therefore, the bases can be ignored and the resulting equation becomes:

n-2 =3

you can add two to both sides and the answer becomes:

n=5.

chrisyhsun | Student, College Freshman | (Level 1) Salutatorian

Posted on

First, let x = n-2. With substitution, we now have 3^x = 27.

We know that x must equal 3, whether that's because the fact is memorized or because 27 divided by 3 produces 1 after dividing three times.

Therefore, x = 3 = n-2.

3 = n-2      (add 2 to both sides)

5 = n

mehran1234 | Student, Grade 7 | eNotes Newbie

Posted on

At first we know that.........

3^3= 27 So therefore we can write....

3^n-2 = 3^3 next

n-2 = 3. After that, you would add 2 on either side to get n = 5.

Soo we get n=5!!

aishukul | Student, Grade 10 | (Level 3) Honors

Posted on

Since 3^3=27, you can replace the 27 in the equation with 3^3:

`=3^3`

Now you can cancel out the bases since they are the same number. You are left with:

n-2=3

n=5. This is the answer.

atyourservice | Student, Grade 11 | (Level 3) Valedictorian

Posted on

When we solve for exponents it is easier if the bases are the same:

We know that 27 can be simplified as `3^3 ` because `3 x 3 x 3 = 27`

set the exponents equal to each other:

`3^(n-2) = 3^3`

`n - 2 = 3`

get n alone by adding 2 to both sides:

`n = 5`

ssandhu05 | Student, Undergraduate | (Level 2) Honors

Posted on

To solve this question, you would have to make sure that the numbers on either side of the equal sign have the same base. 27 also equals 3^3, so therefore you can write 3^n-2 = 3^3. Then, taking out the bases (since they are the same), you would be left with n-2 = 3. After that, you would add 2 on either side to get n = 5.

robertmorgan05 | Student, Grade 12 | eNotes Newbie

Posted on

n=5

We know that 3^3=27, so set the equation up to be n-2=3. To solve this equation, add two to both sides and you get n=5.