Log graphs

[khalil]

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!

[dekoyl]

You can convert it to base e via

[khalil]

True. But wouldn't that just make if more complicated to graph?

[dekoyl]

Can you post the question?

[moshi]

sketch y = log0.5(|2x - 2|) *base 0.5

[GerrySly]

sketch y = log0.5(|2x - 2|) *base 0.5

Sketch without the aid of a calculator

[kamil9876]

And no more base 0.5 (if that is your main concern).

[bem9]

i just found one x intercept, x=1.5, drew that half then reflected it in the y axis because of the mod, is that right?

[Damo17]

sketch y = log0.5(|2x - 2|) *base 0.5

x-intercept:
solve , so
solve , so

y-intercept: let


Asymptote:

and sketch from there.

[khalil]

And no more base 0.5 (if that is your main concern).

But would that method work if they base were, say, 2/5?

[kamil9876]

generalisation:









In fact you can also use dekoyl's change of base formula:



and set which implies , subbing this in gives:

[ngRISING]

wow, thats some intense log stuff. we should know all of this right?

[QuantumJG]

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!

 

[ngRISING]

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.

[TrueTears]

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.

He is saying to just pick points and you should be able to intuitively "guess" the value of a log function.