Post by: khalil on September 27, 2009, 01:45:39 pm
In derrick ha's notes it asks to sketch a graph with base 0.5, I haven't seen that in any textbook!
Post by: dekoyl on September 27, 2009, 02:12:25 pm
Post by: khalil on September 27, 2009, 02:18:55 pm
Post by: dekoyl on September 27, 2009, 02:23:27 pm
Post by: moshi on September 27, 2009, 02:28:18 pm
Post by: GerrySly on September 27, 2009, 02:33:10 pm
sketch y = log0.5(|2x - 2|) *base 0.5Sketch
Post by: kamil9876 on September 27, 2009, 02:35:57 pm
And no more base 0.5 (if that is your main concern).
Post by: bem9 on September 27, 2009, 02:37:34 pm
Post by: Damo17 on September 27, 2009, 02:46:56 pm
sketch y = log0.5(|2x - 2|) *base 0.5
x-intercept:
solve
solve
y-intercept: let
Asymptote:
and sketch from there.
Post by: khalil on September 27, 2009, 02:55:32 pm
And no more base 0.5 (if that is your main concern).
But would that method work if they base were, say, 2/5?
Post by: kamil9876 on September 27, 2009, 03:28:59 pm
In fact you can also use dekoyl's change of base formula:
and set
Post by: ngRISING on September 27, 2009, 04:06:41 pm
Post by: QuantumJG on September 27, 2009, 04:59:44 pm
Are we supposed to know how to sketch log graphs with base x or between zero and 1?
In derrick ha's notes it asks to sketch a graph with base 0.5, I haven't seen that in any textbook!
With logs all you need to know what to do is to find say what:
log_2(5) = some value (I know this is required knowledge fo maths methods)
intuitively you know your answer should be between 2 & 3.
I'm not 100% sure if this is required, but last year we weren't examined on this.
If you were asked to graph log_2(x), pick common points:
x=1,2,4,8,16,32,64,128 that will give: 0,1,2,3,4,5,6,7 for the log_2(x)
if you pick a fraction base, the answer is just the negative of the log_reciprical of the log's original base
I.e. for log_0.5(x) = -log_2(x),
if x=...,1,2,4,8,16,... then log_0.5(x)=...,0,-1,-2,-3,-4,...
or log_2/3(x) = -log_3/2(x) (not that this is more useful)
but for log_1/a(x), this is useful if a is some positive integer like: 1,2,3 because you can graph these logs by just knowing that 2^2 = 4 or 3^3 = 27 and develop a trend.
*EDITED: This edit was to clear up any things that didn't make sense and some errors!
Post by: ngRISING on September 27, 2009, 06:47:59 pm
With logs all you need to know what to do is to find say what:
log_2(5) =
with this you know your answer should be between 2 & 3.
If you were asked to graph log_2(x), pick common points:
x=1,2,4,8,16,32,64,128 will give:0,1,2,3,4,5,6,7
if you pick a fraction base, the answer is just the negative of the log of it's denominator
I.e. log_0.5(x),
if x=...,1,2,4,8,16,... then log_0.5(x)=...,0,-1,-2,-3,-4,...
wait, what? come again. ima tad slow.
Post by: TrueTears on September 27, 2009, 06:48:48 pm
He is saying to just pick points and you should be able to intuitively "guess" the value of a log function.With logs all you need to know what to do is to find say what:
log_2(5) =
with this you know your answer should be between 2 & 3.
If you were asked to graph log_2(x), pick common points:
x=1,2,4,8,16,32,64,128 will give:0,1,2,3,4,5,6,7
if you pick a fraction base, the answer is just the negative of the log of it's denominator
I.e. log_0.5(x),
if x=...,1,2,4,8,16,... then log_0.5(x)=...,0,-1,-2,-3,-4,...
wait, what? come again. ima tad slow.
Post by: ngRISING on September 27, 2009, 07:02:53 pm
sketch y = log0.5(|2x - 2|) *base 0.5
x-intercept:
solve, so
solve, so
y-intercept: let
Asymptote:
and sketch from there.
the x-axis asymtope is from the modulus in the brackets right. rusty on logs. :S
2x-2=0
x=1
Post by: Flaming_Arrow on September 27, 2009, 07:04:46 pm
sketch y = log0.5(|2x - 2|) *base 0.5
x-intercept:
solve
solve
y-intercept: let
Asymptote:
and sketch from there.
the x-axis asymtope is from the modulus in the brackets right. rusty on logs. :S
2x-2=0
x=1
correct
Post by: ngRISING on September 27, 2009, 07:14:06 pm
(http://img41.imageshack.us/img41/7453/81218288.jpg)
can someone explain to me why the correct answers like that T_T>
Post by: TrueTears on September 27, 2009, 07:16:49 pm
generalisation:Really can't put it anyway better than kamil did.
In fact you can also use dekoyl's change of base formula:
and setwhich implies
, subbing this in gives:
Post by: ngRISING on September 27, 2009, 07:18:23 pm
sketch y = log0.5(|2x - 2|) *base 0.5
x-intercept:
solve
solve
y-intercept: let
Asymptote:
and sketch from there.
the y-int is -1. can someone also explain this ^^
Post by: TrueTears on September 27, 2009, 07:20:45 pm
Post by: QuantumJG on September 27, 2009, 07:35:09 pm
sketch y = log0.5(|2x - 2|) *base 0.5
x-intercept:
solve
solve
y-intercept: let
Asymptote:
and sketch from there.
the y-int is -1. can someone also explain this ^^
When graphing something, look and see if it makes logical sense!
If I have a fraction and put it to the power of 1 and then to the power of 2, which is larger?
Obviously the fomer is larger than the latter, but what you have said in your graph is that:
(1/2) < (1/2)^2