Solve for n: `3^(5n + 3) = 3^33`

Expert Answers
Neethu Nair eNotes educator| Certified Educator


We have to find the value of n.

Comparing the left hand side and the right hand side we can write,


i.e. 5n = 33-3


which means n=6

vamkitten | Student





sa122w | Student

Start by looking at the bases on both sides of the equation. In both cases they are three so that makes things easier, since we can drop them. Thus the new equation now becomes 5n+3=33. Now we just have to solve for n, which is basic algebra. 5n+3-3=33-3 (subtract three from both sides). 5n=30. Now divide both sides by 5 and you are left with, N=6. With these type of questions you could always check if you are right by plugging in the value of n into the original equation.

iamkaori | Student

Since both sides of the equation have the same base of 3, you can rewrite the equation as:

5n + 3 = 33

by eliminating the 3's from each side. 

Then, subtract 3 from both sides making

5n = 30

Divide each side by 5 to get


There is the final answer, n is equal to 6.

aishukul | Student

Since both sides of the equation have the same bases (3), you can simply solve for n using the exponents.



n=6. The answer is 6.

ssandhu05 | Student

Well, the numbers on both side of the equal sign have the same base, which is 3. Once you have identified that they have the same base, you can take them out so that it reads 5n + 3 = 33. Then you solve the problem using algebra. You would subtract 3 from both sides to get 5n = 30. Then you would divide 5 from both sides to get n = 6.

atyourservice | Student

The bases (3) are the same so we only need to worry about the exponents.

The first step is to set the exponents equal to each other:

`5n + 3 = 33`

move like terms to the same side by subtracting 3 on both sides:

`5n = 30`

the goal of this problem is to solve for n and since 5 is in the way we have to also divide by 5:

`((5n)/5) = 30/5`

n = 6

to check plug in 6 as nL

`3^(5(6)+3) = 3^33`


`3^33 = 3^33`