Logarithmic equation

[caligirl350]

Evaluate the logarithmic equation for three values of x that are greater than -3, three values of x that are between -4 and -3, and at x = -3. State the equation of the line asymptotic to the graph (if any).
y = -log4 (x + 4)



I don't understand if I am supposed to figure out the problem for x? If anyone could help me out it would greatly be appreciated.

 

[Aladdin]

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For x>-3 , let's take x=0 , x=1 and x=2 ~ Replace each value .



For -4 < x < -3 , let's take x=-3.5 , x=-3.2 and x= -3.8 ~ Replace each value .



For x =-3 .


You must conclude something after you replace the above values , are they in increasing order are they in decreasing order .... etc .

 

[JeffWest]

Hi CaliGirl,

From what I understand the questions is asking is to evaluate the log function at the three different values. You should then be able to plot the graph by hand or you could as well plot it on a graphing calculator.

When you typed in the equation \(\displaystyle y=-log4(x+4)\) do you mean log base 4 written as \(\displaystyle y=-log_4(x+4)\) or \(\displaystyle log(4(x+4))\)

That make a difference.

if you see a log function with no subscript it means that it is in base 10. Your calculator is in base 10.


if you wish to convert to use your calculator here is the equation:

\(\displaystyle log_a(x)=\frac{log_b(x)}{log_b(a)}\) for your problem a would be 4 and b would be 10 because you are are wanting base 4 but the calculator calculates in base 10.

 

[caligirl350]

It is the second way that you had written.

 

[JeffWest]

Great then you don't need to use any of the conversion that I showed.

Is everything clear?

 

[caligirl350]

No, can you help me clear my cloudy brain?

 

[Aladdin]

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""You should then be able to plot the graph by hand or you could as well plot it on a graphing calculator.""

Plot the points ~