I have two questions that needs to be solved with algebra, please help, i figured out the answers to be -4 for the first and -1 for the second but i dont know the steps solving it with algebra.

2^{x}= 1/16 Find X

(0.5)^{x}= 2 Find X

Printable View

- Jul 17th 2012, 03:59 AMTheElectIndices Algebra
I have two questions that needs to be solved with algebra, please help, i figured out the answers to be -4 for the first and -1 for the second but i dont know the steps solving it with algebra.

2^{x}= 1/16 Find X

(0.5)^{x}= 2 Find X - Jul 17th 2012, 04:19 AMProve ItRe: Indices Algebra
- Jul 17th 2012, 04:34 AMTheElectRe: Indices Algebra
Thankyou, but can you please explain further into how that works? Sorry, my understanding of indices aren't that good

- Jul 17th 2012, 04:52 AMProve ItRe: Indices Algebra
- Jul 17th 2012, 07:05 AMHallsofIvyRe: Indices Algebra
Your problem seems to be not understanding what "indices" (I would say "exponents" which is a little more specific than "indices") mean.$\displaystyle x^2$ ('x squared') means 'x times x', $\displaystyle x^3$ means 'x times x times x', etc. Further, a

**negative**exponent means "reciprocal" or "1 over" the value. In particular $\displaystyle 2^4= 2(2)(2)(2)= 16$ so that $\displaystyle 2^{-4}= \frac{1}{16}$.

Of course, $\displaystyle 0.5= \frac{1}{2}$ so that $\displaystyle 0.5= \left(\frac{1}{2^1}\right)= 2^{-1}$ and $\displaystyle (0.5)^x= (2^{-1})^x= 2^{-x}$

So the first equation says $\displaystyle 2^x= 2^{-4}$ and comparing the two sides x= -4.

The second equation says $\displaystyle 2^{-x}= 2^1$ and comparing the two sides gives -x= 1.

(There is a technical point here- that the exponential function is "one-to-one" which means that if f(x)= f(y) then x= y. Not all functions have that property but the exponential does. All you need to know is that you**can**do that for exponential functions.) - Jul 17th 2012, 08:49 AMWilmerRe: Indices Algebra
4^x = 4^y

Can you "see" that x=y?

Let x=2: 4^2 = 16; so 4^y = 16; so y HAS TO equal x : capish? - Jul 17th 2012, 11:51 PMTheElectRe: Indices Algebra
I think I understand now, thanks all of you :)

- Jul 18th 2012, 08:52 AMhemvaneziRe: Indices Algebra
Definition of exponentiation: b^m = b * b * b * … * b (b times itself m times)

For example: b^4 × b^3 =

( b × b × b × b) × ( b × b × b) = (definition of exponentiation)

b × b × b × b × b × b × b = (associative property of multiplication)

b^7 (definition of exponentiation)

If b^m=b^n

b^m/b^n=1

b^(m-n)=1

m-n=0

Hence, m=n