Thread: Indices 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

Originally Posted by TheElect

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

Thankyou, but can you please explain further into how that works? Sorry, my understanding of indices aren't that good

Originally Posted by TheElect

Thankyou, but can you please explain further into how that works? Sorry, my understanding of indices aren't that good

That was every step. I don't know what else I can show you...

Your problem seems to be not understanding what "indices" (I would say "exponents" which is a little more specific than "indices") mean. ('x squared') means 'x times x', means 'x times x times x', etc. Further, a negative exponent means "reciprocal" or "1 over" the value. In particular so that .

Of course, so that and

So the first equation says and comparing the two sides x= -4.

The second equation says 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.)

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?

I think I understand now, thanks all of you

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