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logarithmic function helpppp :(

0 votes
The graph below shows the logarithmic function y=log2 x. identify the domain and Range.

- What is the value of the x-intercept?

-Explain why the x-intercept of a logarithmic function will always have this value

-In details why a logarithmic function will never have a y- intercept.

-explain why (8,3) exists as a point on this graph based on your knowledge of exponential function.
asked Dec 10, 2014 in CALCULUS by anonymous

i forgot the graph :) 

4 Answers

0 votes

(a)

The function is log2(x).

Let y = log2(x)

As the logarithmic function is not defined for the negative values of x.

Then domain of the function is (0, ∞)

Range of the function is the value of function for different values of x.

Range of the function is (-∞, ∞).

Therefore,

Domain is (0, ∞).

Range is (-∞, ∞).

answered Dec 10, 2014 by Lucy Mentor
0 votes

(b)

The function is log2(x).

Let y = log2(x)

To find the x - intercept of the function, substitute y = 0 in the function.

log2(x) = 0

log(x)/log(2) = 0                (Using logaritmic properties loga(b) = log(b)/log(a))

log(x) = 0

log(x) = log(1)

Cancel the logarithm on each sides.

x = 1

Therefore the x - intercept of the function is x = 1.

That is why x intercept of logarithmic function always has a value x = 1.

answered Dec 10, 2014 by Lucy Mentor
edited Dec 10, 2014 by Lucy
0 votes

(c)

The function is log2(x).

Let y = log2(x)

To find the y intercept of the function, we need to substitute x = 0 in the function.

we know that the value of loagrithmic function at x = 0 is undefined.

Therefore there is no y intercept.

answered Dec 10, 2014 by Lucy Mentor
0 votes

(d)

The function is log2(x).

let y = log2(x)

Now let us consider x = 8

x = 8 is in the domain of function

y = log2(8)

y = log2(2³)

y =3*log2(2)

y = 3.             (log2(2) = 1)

y = 3 is in the range of function

Point (8,3) exists.

Graph

Therefore we can observe that the point (8,3) exists.

answered Dec 10, 2014 by Lucy Mentor
edited Dec 10, 2014 by Lucy

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