Question

y=log(base10)^3-4x? ....trying to figure out how to start?... any help is appreciated

Answer 1

Solve for x?

Answer 2

I'm actually trying to just put it into exponential form so I can figure out the graph and find the domain. I guess I should of included that.

Answer 3

If \[\Large \log_{b} a = c\] then:
\[\Large a = b ^{c}\]

Answer 4

\[\Large \log_{10} (3 - 4x) = y\]Therefore\[\Large (3 - 4x) = 10^{y}\]

Answer 5

Ok. so 3-4x=10^x?

Answer 6

Ohhhhh....:) ok. thank you. I super appreciate it.

Answer 7

^^^ the right side side should be 10^y

Answer 8

But to graph it you don't need to put it in an exponential form. You are already given y as a function of x and so you can find the domain and graph it without having to put it in exponential form.

Answer 9

Oh. Well how does the 3-4x change the behavior of the graph does is reflect it across the x axis or is it still the same behavior as log b of x just as x>0 the line is increasing or decreasing?

Answer 10

First figure out the domain.
The rule is you cannot take the logarithm of zero or a negative number.
Can you figure out the domain here?

Answer 11

oh. yes. I figured it out. I would set 3-4x>0
-3 -3
-4x>-3
/-4 /-4
x< 3/4
domain: (-infi.- 3/4)

Answer 12

Good.
We know that x = 3/4 is a vertical asymptote for this function because when x approaches 3/4 we are approaching closer to log(0) which is negative infinity.

So try a few values of x < 3/4 such as 0, -1, -2, etc.
Knowing the general curve of a logarithmic function and knowing the vertical asymptote and a few points you can graph the function.

Answer 13

great. thank you.

Answer 14

you are welcome.