how do i determine if a function is exponential or logarithmic if im only given the domain and range

- anonymous

how do i determine if a function is exponential or logarithmic if im only given the domain and range

- jamiebookeater

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- anonymous

exponents have an infinite domain and finite range
logarithms have a finite domain and infinite range

- anonymous

it gave me D={-2, -2, 0, 1, 2} R={0.25, 1, 4, 16, 64}

- anonymous

This is not a function as -2 must map to two different values in the range and functions only have one output for any given input

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- anonymous

the problem just shows that and asks whether it logarithmic or exponential

- anonymous

If you meant -1 then this is exponential, if you plot the data it starts to increase slowly and then speeds up

- anonymous

what about
D={0.25, 1, 4, 16, 64}
R={-2, -1, 0, 1, 2}

- anonymous

(although all logarithmic functions are, are simply the inverse of an exponential function, so technically all logarithmic functions are exponential as well.

- anonymous

in that one they changed the domain and range so the first was exponential, this one is the inverse so it must be logarithmic.

- anonymous

and how can i tell if a graph is logarithmic or exponential if im only given a graph, nothing else

- anonymous

If it starts off flat and then curves up (or down) it's exponential.
If it starts off going up (or down) and flattens out it's logarithmic.

- anonymous

oh! ok, thank you :) do you know anything about equations containing radicals and exponents by any chance?

- anonymous

Ohhh, I know a thing or two about those guys. :)

- anonymous

how would i solve 1/4^3x=2

- anonymous

Is it:\[(1/4)^{3x}=2\]

- anonymous

the x isnt attatched to the exponent,

- anonymous

ok so:
\[(1/4)^{3}x=2\]

- anonymous

yes, and the fraction isnt in parenthesis

- anonymous

First raise 1/4 to the third power:
1/4^3 = 1/64 (4^3 = 4*4*4)
so 1/64x = 2
multiply both sides by 64
x = 128

- anonymous

wait i made a mistake, its 1/4x^3=2

- anonymous

oh, that makes a little bit of a difference...
First multiply both sides by 4
x^3 = 8
next raise both sides to the (1/3) power
x = (8)^(1/3)
x = 2

- anonymous

wht if i had 1/8x^6-3=5

- anonymous

Working backwards get rid of the -3 first
1/8x^6 = 8
next multiply by 8
x^6 = 64
now raise both sides to the 1/6 power
x = (64)^(1/6)
x = 2

- anonymous

One way to get rid of exponents is to raise both sides to 1/n where n is the exponent.

- anonymous

how come i have to make the exponent 1/6?

- anonymous

oh! ok, but how does it equal to 2

- anonymous

if you have a calculator you can type in 64^(1/6) and it should give you the answer of 2.
Or you can ask yourself what number times itself 6 times is 64? And then use guess and check to find 2. (I like the calculator way myself)

- anonymous

oh i see, what do i do if i have (x-1)^2/3-13=3
i know i have to add 13 to both sides but what do i do with the exponent

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