anonymous
  • anonymous
how do i determine if a function is exponential or logarithmic if im only given the domain and range
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
exponents have an infinite domain and finite range logarithms have a finite domain and infinite range
anonymous
  • anonymous
it gave me D={-2, -2, 0, 1, 2} R={0.25, 1, 4, 16, 64}
anonymous
  • 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
  • anonymous
the problem just shows that and asks whether it logarithmic or exponential
anonymous
  • anonymous
If you meant -1 then this is exponential, if you plot the data it starts to increase slowly and then speeds up
anonymous
  • anonymous
what about D={0.25, 1, 4, 16, 64} R={-2, -1, 0, 1, 2}
anonymous
  • anonymous
(although all logarithmic functions are, are simply the inverse of an exponential function, so technically all logarithmic functions are exponential as well.
anonymous
  • 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
  • anonymous
and how can i tell if a graph is logarithmic or exponential if im only given a graph, nothing else
anonymous
  • 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
  • anonymous
oh! ok, thank you :) do you know anything about equations containing radicals and exponents by any chance?
anonymous
  • anonymous
Ohhh, I know a thing or two about those guys. :)
anonymous
  • anonymous
how would i solve 1/4^3x=2
anonymous
  • anonymous
Is it:\[(1/4)^{3x}=2\]
anonymous
  • anonymous
the x isnt attatched to the exponent,
anonymous
  • anonymous
ok so: \[(1/4)^{3}x=2\]
anonymous
  • anonymous
yes, and the fraction isnt in parenthesis
anonymous
  • 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
  • anonymous
wait i made a mistake, its 1/4x^3=2
anonymous
  • 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
  • anonymous
wht if i had 1/8x^6-3=5
anonymous
  • 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
  • anonymous
One way to get rid of exponents is to raise both sides to 1/n where n is the exponent.
anonymous
  • anonymous
how come i have to make the exponent 1/6?
anonymous
  • anonymous
oh! ok, but how does it equal to 2
anonymous
  • 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
  • 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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