A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 3 years ago
3^5n=3^5(3^2n)^2 solve for n
anonymous
 3 years ago
3^5n=3^5(3^2n)^2 solve for n

This Question is Closed

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Please rewrite the question using the equation tool, as it's tough to tell if you mean: \[3^{5n}\] or \[3^{5}n\] for example. Same thing goes for the other side of the equation.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0its the first one 5n is on three

KingGeorge
 3 years ago
Best ResponseYou've already chosen the best response.1\[3^{5n}=3^5\cdot(3^{2n})^2\]Correct?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[3^{5n}=3^{5}(3^{2n})^{2} solve for n\]

KingGeorge
 3 years ago
Best ResponseYou've already chosen the best response.1First, you need to simplify the expression on the right side. Recall that \[(a^b)^c=a^{bc}\]This means that you can rewrite the right hand side as \[3^5\cdot3^{4n}\]

KingGeorge
 3 years ago
Best ResponseYou've already chosen the best response.1Now we also have the rule that \[a^b\cdot a^c=a^{b+c}\]That means we can rewrite the RHS again. This time as \[3^{5+4n}.\]That means we have the relation \[3^{5n}=3^{5+4n}\]

KingGeorge
 3 years ago
Best ResponseYou've already chosen the best response.1Since 3 is the base on both sides, we can just get rid of it (otherwise known as taking the log base 3 of both sides). Hence, we only have to solve the equation \[5n=5+4n\]Can you do this yourself?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0wait im confused like if its (3xy)^3 then the "3" would be 27 but there the 3 is still "3" whys that?

KingGeorge
 3 years ago
Best ResponseYou've already chosen the best response.1In the case of \((3xy)^3\), you can think of it as \[(3xy)(3xy)(3xy)=(3\cdot3\cdot3)\cdot(x\cdot x\cdot x)\cdot(y\cdot y\cdot y)=3^3\cdot x^3\cdot y^3=27x^3y^3\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0oh hey can u help me on this prob? \[3*9^{2n}=(3^{n+1})^{3}\]

KingGeorge
 3 years ago
Best ResponseYou've already chosen the best response.1First off, write \[3\cdot9^{2n} =3\cdot(3^2)^{2n}\]Can you show the next step in simplifying this?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0ok um its \[(3^{2n+1}) on the \right side im confused for the \left side\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0It may help you if you temporarily replace the exponents with simpler variables. For example, you could say 2n = X, and n+1 = Y. That way you can rewrite that equation as: \[3*9^{x} = (3^{y})^{3}\] From there you can use the rules George posted.

KingGeorge
 3 years ago
Best ResponseYou've already chosen the best response.1Wait, on the right side, you have\[\Large (3^{n+1})^3\]What you gave, was a simplification for \[\Large (3^{n+1})^2\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0oh yeah my bad yeah its 3

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0please i get the right side is 3^3n+3 but what i do to the rigleft side?

KingGeorge
 3 years ago
Best ResponseYou've already chosen the best response.1For the left side, we have \[\large 3\cdot(3^2)^{2n}\]Using the same principles you just used for the right side, what is \[\large (3^2)^{2n}?\]

KingGeorge
 3 years ago
Best ResponseYou've already chosen the best response.1Perfect. Now what is \[\large 3\cdot3^{4n}?\]

KingGeorge
 3 years ago
Best ResponseYou've already chosen the best response.1Right again. That means we can take log base 3 of both sides, and get \[4n+1=3n+3\]From here, it's just a simple solving of a linear equation.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0FYI if you do substitute 2n = X, and n+1 = Y: \[3*9^{x} = 3^{3y}\] Since \[9 = 3^{2}\] \[3*(3^{2})^{x} = 3^{3y}\] \[3*3^{2x} = 3^{3y}\] \[3^{1}*3^{2x} = 3^{3y}\] \[3^{2x+1} = 3^{3y}\] Take the log base 3 of both sides to get: 2x+1 = 3y Replace x and y with their values to get: 2(2n)+1 = 3(n+1) 4n+1 = 3n+3

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0oh thank you very much hey one more

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0why is 3 in (3xy)^3 is 27... but 3in (3^2n)^2 is still 3 ?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0You may want to start a new question for each question to make it easier to read for others later on.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Is that \[(3^{2n})^{2}\] ?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0is it because we treat 3 as an x? so 3 doesnt change?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0and also usually the 3 has a degree of 0 but here it is one

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[3^{4n}\] Because you don't know what the full exponent is, it's easier to keep it as it is. You could rewrite it as \[(3^{4})^{n}\] and then solve for 3^4, so you'd get: \[81^{n}\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.03 has a degree of 0, huh?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0in the degree of a monomial the constant has a degree of 0 right?

KingGeorge
 3 years ago
Best ResponseYou've already chosen the best response.1It's not the constant that has a degree, it's the variable that has degree 0. Because the degree is 0, the variable can be replaced with \(x^0=1\), so you see a constant term.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.