Question

Can somebody help my poor little soul?

Answer 1

\[2^{2n}+2^{2n}+2^{2n}+2^{2n}=4^{24}\]

Answer 2

wouldn't it be (2^2)24 and then you multiply 2 to 24?

Answer 3

\[\large \bf 2^{2(n)}+2^{2(n)}+2^{2(n)}+2^{2(n)}=4^{24}\]
\[\large \bf 4^n+4^n+4^n+4^n=4^{24}\]
Since,their bases are same,so we are required to equal the powers of base,

\[\large \bf n+n+n+n=24\]
\[\large \bf 4n=24\]
\[\large \bf n=\frac{24}{4}=6=\color{red}{Answer}\]

Answer 4

hope you understand. @yomamabf

Answer 5

dude.... it says the answer is 23 tho....

Answer 6

oh!! Ghosh.....sorry :(...

Answer 7

i got the answer :-
Sorry,i made a little mistake

Answer 8

See :-
\[\large \bf 4^n+4^n+4^n+4^n=4^{24}\]
\[\large \bf 4(4^n)=4^{24}\]
\[\large \bf 4^n=\frac{4^{24}}{4}=4^{23}\]

So, n=23

Answer 9

really very very sorry :(... @yomamabf

Answer 10

so understood ?? @yomamabf

Answer 11

is your POOR LITTLE SOUL satisfy ??

Answer 12

I'm trying to understand what you did. So you don't break it down to 2?

Answer 13

\[\large \bf 2^{2n}=2^{2(n)}=4^n\]
I use this ^^^

Answer 14

you do it the complicated way but okay thanks anyway

Answer 15

welcome :)

Answer 16

Another way to look at this ...
$$
\large{
4^{24}=(2\times 2)^{24}}=(2^2)^{24}=2^{2\times 24}\\
$$
Also,
$$
\large{
2^{2n}+2^{2n}+2^{2n}+2^{2n}=4\times 2^{2n}=2^2\times2^{2n}=2^{2 + 2n}
}
$$
This means that
$$
\large{
2^{2\times 24}=2^{2+ 2n}\\
\implies 2\times24=2+2n\\
\implies 48-2=2n\\
\implies \cfrac{46}{2}=n\implies n=23


}
$$

Hope this helps :-)

Answer 17

\large{
4^{24}=(2\times 2)^{24}}=(2^2)^{24}=2^{2\times 24}\\
$$
Also,
$$
\large{
2^{2n}+2^{2n}+2^{2n}+2^{2n}=4\times 2^{2n}=2^2\times2^{2n}=2^{2 + 2n}
}
$$
This means that
$$
\large{
2^{2\times 24}=2^{2+ 2n}\\
\implies 2\times24=2+2n\\
\implies 48-2=2n\\
\implies \cfrac{46}{2}=n\implies n=23