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

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vamkitten | Student, Undergraduate | (Level 1) Honors

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swaathi787 | eNotes Newbie

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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:


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

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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

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mehran1234 | Student, Grade 7 | eNotes Newbie

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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!!

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

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


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


n=5. This is the answer.

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

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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`

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ssandhu05 | Student, Undergraduate | (Level 2) Honors

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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.

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robertmorgan05 | Student, Grade 12 | eNotes Newbie

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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.

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