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WiredBest ResponseYou've already chosen the best response.0
Please 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.
 one year ago

louis413Best ResponseYou've already chosen the best response.0
its the first one 5n is on three
 one year ago

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

louis413Best ResponseYou've already chosen the best response.0
\[3^{5n}=3^{5}(3^{2n})^{2} solve for n\]
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
First, 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 \[3^5\cdot3^{4n}\]
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
Now 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 \[3^{5n}=3^{5+4n}\]
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
Since 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?
 one year ago

louis413Best ResponseYou've already chosen the best response.0
wait im confused like if its (3xy)^3 then the "3" would be 27 but there the 3 is still "3" whys that?
 one year ago

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

louis413Best ResponseYou've already chosen the best response.0
oh hey can u help me on this prob? \[3*9^{2n}=(3^{n+1})^{3}\]
 one year ago

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

louis413Best ResponseYou've already chosen the best response.0
ok um its \[(3^{2n+1}) on the \right side im confused for the \left side\]
 one year ago

WiredBest ResponseYou've already chosen the best response.0
It 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.
 one year ago

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

louis413Best ResponseYou've already chosen the best response.0
oh yeah my bad yeah its 3
 one year ago

louis413Best ResponseYou've already chosen the best response.0
please i get the right side is 3^3n+3 but what i do to the rigleft side?
 one year ago

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

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

KingGeorgeBest ResponseYou've already chosen the best response.1
Right 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.
 one year ago

WiredBest ResponseYou've already chosen the best response.0
FYI 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
 one year ago

louis413Best ResponseYou've already chosen the best response.0
oh thank you very much hey one more
 one year ago

louis413Best ResponseYou've already chosen the best response.0
why is 3 in (3xy)^3 is 27... but 3in (3^2n)^2 is still 3 ?
 one year ago

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

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

louis413Best ResponseYou've already chosen the best response.0
is it because we treat 3 as an x? so 3 doesnt change?
 one year ago

louis413Best ResponseYou've already chosen the best response.0
and also usually the 3 has a degree of 0 but here it is one
 one year ago

WiredBest 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: \[81^{n}\]
 one year ago

WiredBest ResponseYou've already chosen the best response.0
3 has a degree of 0, huh?
 one year ago

louis413Best ResponseYou've already chosen the best response.0
in the degree of a monomial the constant has a degree of 0 right?
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
It'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.
 one year ago
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