Does anyone know what 4^(x-6) = 16^x is?

Question

Does anyone know what 4^(x-6) = 16^x is?

Answer 1

Yes. x = - 6. Here's how to show this:

Since 16 = 4^2, rewrite your eqn. as 4^(x - 6) = 4^(2 x).

The exponents of ' 4 ' must match! Then x - 6 = 2 x; so x = - 6.

CHECK: If x = - 6, x - 6 = -12, so 4^(x - 6) = 4^(-12) = 1(4^12)
= 1/16777216.

Meanwhile 16^(-6) = 1/(16^6) = 1/16777216.

So they're EQUAL. QED

Live long and prosper.

Answer 2

Take the base-4 logarithm of both sides:
|--: x-6 = 2x
|--: x = -6

Double-check the answer:
|--: 4^ ((-6)-6) ?=? 16^(-6)
|--: 4^(-12) = (4^2)^(-6) = 4^(2*(-6)): Yes.

Answer 3

4 = 2^2
16 = 2^4

(2^2)^(x - 6) = (2^4)^x

when you have an exponent to an exponent, you multiply the exponents

2 ^ (2x - 12) = 2^(4x)

since they have the same base, the exponent must be equal to each other

2x - 12 = 4x
-12 = 2x
x = -6

Answer 4

if you are looking for X and if this is ALGEBRA then i think im right..


i do believe the answer is -2...

solution:

4^(x-6) = 16^x



4x-24 = 16x
-24 = 16x - 4x
-24 = 12x
*to have only the x we need to eliminate the 12.. divide both sides by 12..
answer:


-2 = x


checking:

4^(-2-6) = 16^-2
4^-4 = 256
256 = 256

*equal, so my answer is correct! ;]

Answer 5

4^(x-6) = 4^x/4^6
16^x = 4^2x

4^x = 4^6*4^2x

1 = (4^6)*(4^x)

take log of both sides

0 = 6*log(4) + x*log(4)

x = -6

Answer 6

it's x= 22. it's very simple.

Answer 7

65536=x