Answer:
1) Convert it to the same base and make a table with two columns for x, and y values.
2) The greater the base the lower the curve. Check the picture below.
Step-by-step explanation:
1. Remember the rule in order to convert it to the same base two other logarithms:
[tex]log_{a}b=\frac{log_{c}a}{log_{c} b}[/tex]
Example
[tex]log_{5} 20 \\ log_{2} 4\\ \\\frac{log_{10}20}{log_{10}4} =\frac{log2+log10}{log2+log2} = 2,16[/tex]
2. When we make the base bigger and bigger the curve will get closer and closer to the y-axis, such as those logarithmic functions.
Algebraically this is why
[tex]y=log_{2}3=1.58[/tex]
[tex]y=log_{10}3=0.477[/tex]
And so on...
3) Make a table for x values and plug the values to return the y values. Do not forget, x > 0
For [tex]y=log_{2}x[/tex]
x y
1 0
2 1
4 2
[tex]y=log_{10}x[/tex]
x y
1 0
2 0,3
4 0,6
Trace the hyperbole and check for yourself!
