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C1 indices

How would you find x?...

4^x=1/4

thanks :smile:

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Reply 1
Avatar for roar558
roar558
11
Original post by jessica_anne_clu
How would you find x?...

4^x=1/4

thanks :smile:


ln both sides if you want to show it mathmatically.
Reply 2
Avatar for raheem94
raheem94
13
Original post by jessica_anne_clu
How would you find x?...

4^x=1/4

thanks :smile:


e.g.

22x=12[br]22x=2−1[br]2x=−1[br]x=−12[br] 2^{2x} = \frac12 [br]2^{2x} = 2^{-1}[br]2x = -1[br]x = -\dfrac12[br]
Reply 3
Avatar for kingtaco
kingtaco
Original post by jessica_anne_clu
How would you find x?...

4^x=1/4

thanks :smile:


What power would you use to get the reciprocal of a number?
Original post by roar558
ln both sides if you want to show it mathmatically.


but how would you go about it? I know the answer is -1 but I don't know how you'd get it
Reply 5
Avatar for james.h
james.h
11
In this case, try multiplying both sides by 4:

4x+1=14^{x+1}=1

Can you see the answer now? :smile:


A general approach for any question like this involves logarithms, but I don't think they're covered in C1...?
Reply 6
Avatar for steve2005
steve2005
17
Original post by jessica_anne_clu
but how would you go about it? I know the answer is -1 but I don't know how you'd get it


Just write down the answer. No working required.
Reply 7
Avatar for raheem94
raheem94
13
Original post by roar558
ln both sides if you want to show it mathmatically.


ln is in C3, while OP is studying C1 so she probably doesn't knows logarithms.
Reply 8
Avatar for tnetennba
tnetennba
9
You could use logarithms:
Log 4^x = Log 0.25
x Log 4 = Log 0.25
x= (Log 0.25)/(Log 4)
x=-1
:smile:
Reply 9
Avatar for raheem94
raheem94
13
Original post by jessica_anne_clu
but how would you go about it? I know the answer is -1 but I don't know how you'd get it


12=2−1[br]14=?[br] \dfrac12 = 2^{-1}[br]\dfrac14 = ?[br]
Original post by raheem94
e.g.

22x=12[br]22x=2−1[br]2x=−1[br]x=−12[br] 2^{2x} = \frac12 [br]2^{2x} = 2^{-1}[br]2x = -1[br]x = -\dfrac12[br]


x = -1, as

4x = 14\frac{1}{4}
Reply 11
Avatar for raheem94
raheem94
13
Original post by tnetennba
You could use logarithms:
Log 4^x = Log 0.25
x Log 4 = Log 0.25
x= (Log 0.25)/(Log 4)
x=-1
:smile:


OP is studying C1 indices, so she probably doesn't knows logarithms.
Reply 12
Avatar for raheem94
raheem94
13
Original post by thegodofgod
x = -1, as

4x = 14\frac{1}{4}


I didn't wanted to give the solution hence i was giving a similar example, i know the answer for OP's question is -1.
Original post by james.h
In this case, try multiplying both sides by 4:

4x+1=14^{x+1}=1

Can you see the answer now? :smile:


A general approach for any question like this involves logarithms, but I don't think they're covered in C1...?


4x=144^{x}=\frac{1}{4}

22x=142^{2x}=\frac{1}{4}

22x=[12]22^{2x}=[\frac{1}{2}]^2

22x=2−1×22^{2x}=2^{-1 \times 2}

22x=2−22^{2x}=2^{-2}

2x=−22x=-2

x=−1x=-1
Original post by raheem94
OP is studying C1 indices, so she probably doesn't knows logarithms.

You're right :smile: I am studying C2 at the moment but I am retaking C1 :smile:
Original post by raheem94
I didn't wanted to give the solution hence i was giving a similar example, i know the answer for OP's question is -1.


My bad :colondollar:
Reply 16
Avatar for raheem94
raheem94
13
Original post by thegodofgod
4x=144^{x}=\frac{1}{4}

22x=142^{2x}=\frac{1}{4}

22x=[12]22^{2x}=[\frac{1}{2}]^2

22x=2−1×22^{2x}=2^{-1 \times 2}

22x=2−22^{2x}=2^{-2}

2x=−22x=-2

x=−1x=-1


Isn't it easier to do it in the below way:
4x=14[br]4x=4−1[br]x=−1[br] 4^x = \dfrac14[br]4^x = 4^{-1}[br]x=-1[br]
Involves only 2 steps.
Reply 17
Avatar for james.h
james.h
11
Original post by thegodofgod
...full solution...

I did say "for any question". Try that method you've stated on something like ax=1/ba^x = 1/b :p:

I get your point, though. :yep:
Original post by raheem94
Isn't it easier to do it in the below way:
4x=14[br]4x=4−1[br]x=−1[br] 4^x = \dfrac14[br]4^x = 4^{-1}[br]x=-1[br]
Involves only 2 steps.


Hmm - didn't even notice that :giggle:

Think it was a good decision of mine to drop maths after AS :colondollar:
Reply 19
Avatar for Dj.Clay
Dj.Clay
4
Why would you convert everything to powers of 2 when it's already powers of 4? :/

All you do for this question is rewrite 1/4 as 4^(-1) and compare indices.

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