Question

find the value of N that makes 3^4n x 3^n+4=3^14

Answer 1

When you multiply, you keep the powers the same. 4 times ? = 14

Answer 2

I assume you mean \(\large 3^{4n}\times 3^{n+4}=3^{14}\)?

Answer 3

yes

Answer 4

Since we're multiplying exponential terms that have the same base, we can add the exponents to get \(\large 3^{4n+n+4} = 3^{14}\implies 3^{5n+4}=3^{14}\).

At this point, we note that the base of each exponential term is 3; thus, these two sides are equal only if their exponents are equal. All you need to do now is solve \(5n+4=14\) for \(n\).

Can you take things from here? :-)

Answer 5

yes i get it now :)