when do you use the inverse when doing logs?

- anonymous

when do you use the inverse when doing logs?

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- amistre64

log is the inverse of exponents; and exponents are the inverse of logs.
What is your question regarding?

- anonymous

i dont understand how to do them at all. how would you graph y=3log(base5)x. how would you go about that

- anonymous

Hey amistre can you please help me with 2 antiderivative questions after you are done here?

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## More answers

- amistre64

Since y = 3 log5(x) is the same as:
y = log5(x^3) we can more easily graph its inverse and then "flip" the graph about the y=x line.

- amistre64

sure thing...

- amistre64

you got a question posted we can go to :)

- anonymous

did you get the second equation from switching the x and ys and solving for y?

- anonymous

did you see my question

- amistre64

yeah, but I messed it up in my head the first time :)

- anonymous

meet me there when you can help me

- amistre64

will do...

- amistre64

mini: log graphs can be hard to do without a calulator; so we can rewrite it to a more familiar form... do you agree?

- anonymous

but how do you make it in the other form?

- anonymous

im there

- amistre64

y = 3 log5(x) ; divide by 3
y/3 = log5(x) ; take the 5^ of each side
5^(y/3) = 5^(log5(x)) ; 5^(log5) cancel each other out.
5^(y/3) = x
Do you agree? Are you familiar with the rules for logs?

- anonymous

i understand how you did that. when is that that you go about switching the x and y to solve?

- amistre64

When it makes the graphing easier you can modify it. All you are doing is solving for x instead of y, so keep aware of that

- amistre64

Would you agree that 5^(y/3) is easier to plot for and solve than log5(x) ? :)

- anonymous

yess

- anonymous

how do you do for example logbase8 4096=4

- amistre64

Do you mean:
log8(4096) = 4 ??

- anonymous

yes

- anonymous

is it just 8^4=4096

- amistre64

that is what is known as an identity. one side equals the other.
Lets take for example:
logB(x) = y this means that B^y=x
We can take your equation for instance:
log8(4096) = 4 means:
8^4 = 4096, we can test that by either pen and paper , or calculator :)

- anonymous

35^log 35^x

- amistre64

35^log35 = 1 and we are left with "x"

- anonymous

can you do the inverse of y=log1/4 x out step by step please?

- anonymous

y=ln 6x

- amistre64

is that log base (1/4)?

- anonymous

i understand that one now but how do you do the second one?

- amistre64

y = ln(6x) correct?

- anonymous

just y= ln 6x not base 6x

- amistre64

"ln" is just a special way they write log to the base "e"

- amistre64

y = ln(6x)
e^y = e^ln(6x)
e^y = 6x
(e^y)/6 = x

- anonymous

how about y= ln (x+2)

- amistre64

e^y = x+2
e^y -2 = x

- anonymous

so for the graph of y=log8 x-2
you would do
8^y=x-2
and then fill in values for y such as 0
which would be
1=x-2
x=3?

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