Find the graph ofthe function ylogx311 Then state its domain

Find the graph ofthe function y-log(x-31-1 Then state it\'s domain range and asymptote c. d. Find the domain of the function. 30888 3 4

Solution

log 3 (x - 3) - 1

We know that x - 3 > 0 for domain
x > 3

Range :
For any log function of the form log(ax + b) + C, etc
range is ALWAYS All reals

Graph is option C

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x^2 + 3x > 0

x(x + 3) > 0

Key values are 0 and -3

Region 1(-inf , -3)
Test = -4
x^2 + 3x comes out positive for x = -4
So, this works as tis positive....

Region 2 : (-3,0)
Test = -1
Doesnt work cuz x^2 + 3x < 0

Region 3 : (0 , inf)
Works!

So, domain :
(-inf , -3) U (0, inf)

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5)
10 ^(log(pi)

The 10^and log cancel out...

pi ---> ANS

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6)
ln(e^(4x))

ln and e together annhilate and canel out....

4x

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(1/2)^-4 = 16

In log form this is ....

log (base 16) 1/2 = -4 ---> ANS

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log (base 8) 4

We can write this as ....

ln(4) / ln(8)

ln(2^2) / ln(2^3)

Using exponent law, we get :
2ln(2) / 3ln(2)

2/3 ---> ANS

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