Question

Can I know how to solve this problem????The question is 4^x/16=64/2^y

Answer 1

Hey @Babypanda

What do you have to solve for in this question? :)

Answer 2

WELL MY ANSWER WAS x=3 AND Y=4 but my friend said the answer is WRONG!!!!

Answer 3

AkashdeepDeb are you having a deep thought about the question??????

Answer 4

Try putting those values into the equation, if you get the answer, you are right, if you don't, your friend is.

Go ahead, like this:
\[\frac{4^x}{16} = \frac{64}{2^y}\]
Cross multiply.
\[4^x . 2^y = 64.16\] NOTE: [The dot implies multiplication]

Now express this in powers of '2'. Because all the numbers you see are powers of 2! :D
\[2^{2x}~.~2^y = 2^6~.~2^4\]
Now let's use some exponents' rules.
We know that, \(~~~a^x~.~a^y = a^{x+y}\)
So, \(~~~a^{any~number}~.~a^{some ~number} = a^{any~ number~ + ~some ~number}\)

Thus, then our equation becomes,

\[2^{2x+y} = 2^{10}\]
Now, since the base [2] is the same, even the exponent MUST be the same, right?
Becuase, if \(~~~a^(x) = a^(y)\) then \(x\) must be equal to \(y\). :D

So, we get, 2x + y = 10.
Now if we have another equation for x and y, we can find the value of x,y.

Understood this? :)

Answer 5

By the way -
That is, \[a^x = a^y,~ ~then~ ~x~~ must ~~be~~ equal~~ to~~ y\]

Answer 6

Thank you so much!!!!!! The question that links to it is log x ( y+2)=1 + log x 4

Answer 7

Well, you can another equation from that, do you know how to solve that? ^

Answer 8

...can (get) another...

Answer 9

Is it y=4x -2....The answer for the second equation...

Answer 10

Is this the equation: \(~~~log~{x(y+2)} = 1 + log~(x^4)\) ?

Answer 11

NO!!!!It is log x\[\log_{x}(y+2)=1+\log_{x}4 \]

Answer 12

One sec...

Answer 13

OKAY

Answer 14

y = 4x - 2 is right. :)
Now solve the equations and see what you get.

Answer 15

Is it x = 6 and y= 22????

Answer 16

No. Check again.
That does not satisfy the first equation. :)
x=2
y=6

Answer 17

Yeah !!!! YOU ARE RIGHT !!!! i WROTE THE WRONG EQUATION.....
THANK YOU!!!!

Answer 18

ARE YOU A FORM 5 STUDENT????

Answer 19

I am not sure what that is. Yes, but I am a student.

Answer 20

WAIT , you are not from Malaysia???

Answer 21

Haha, no.

Answer 22

So,all this while I was talking to a foreigner...Cool..

Answer 23

Well,in our country form 5 means you are 17 years old teenager.....

Answer 24

Informative. Thanks for letting me know.
I am 16 years old.

Answer 25

Well, you as same age as me...
Nice to know you genius