Question

Solve for n: (4^n)^3 (2^n + 2) = (42)^n – 1.

A. –2

B. –1

C. 0

D. 2

Answer 1

interesting

Answer 2

for clarification's sake \[\huge (4^n)^3 (2^{n+2}) = 42^{n-1}\]
yes?

Answer 3

\[(4^{n})^{3} (2^{n+2}) = (4^{2}) ^{n-1}\]

Answer 4

that makes it a lot easier

Answer 5

you can use trail and error method..

Answer 6

first, simplify the (4^n )^3 so you have 4^(3n) agree?

Answer 7

(trial and error works too since this is multiple choice btw)

Answer 8

after simplifying 4^3n, how do I continue?

Answer 9

4^(3n)=2^6n....agree?

Answer 10

^that

Answer 11

put everything in base of 2

Answer 12

why 2^6n? I dont understand

Answer 13

\[4^{3n}=(2^{2})^{3n}=2^{6n}\]

Answer 14

\[(a ^{x})^{y}=a ^{xy}\]

Answer 15

Ok I understand now!

Answer 16

\[2^{6n} x 2^{n+2} = (4^{2})^{n-1}\]

Answer 17

How do I continue?

Answer 18

now...\[a ^{x}*a^{y}=a ^{x+y}\]

Answer 19

I dont understand! :(

Answer 20

okay...tell me a*a*a*a=?

Answer 21

no..its a*a*a*a=a^4

Answer 22

6n x 2n + 2 = 2n-1

Answer 23

is this correct?

Answer 24

what you said is ....a+a+a+a=4a

Answer 25

Yes I understand the mistake I made

Answer 26

okay now \[2^{6n}*2^{n+2}=?\]

Answer 27

6n + n+2

Answer 28

well done...its 2^(6n+n+2)=2^(7n+2)

Answer 29

now right hand side...
\[4^{2}^(n-1) = ?\]

Answer 30

it is like...\[(a ^{x})^{y}=a ^{xy}\]

Answer 31

4^2n-2 ?

Answer 32

good...now \[(2^{2})^{2n-2}=?\]

Answer 33

2^4n+4 ?

Answer 34

there is minus sign...so 2^(4n-4)
now...7n+2=4n-4.....as they all in equal base...

Answer 35

is -2 the answer?

Answer 36

yep..correct !

Answer 37

Thanks a lot!

Answer 38

you are welcome...