MIDTERM #2

SOLVING LOGARITHMIC/EXPONENTIAL EQUATIONS

100

ln e=x

1/25= 5^x

x=1

x=-2

200

log₂(x-3)=-1

x=7/2

300

log(7x+1) = log(6x-5)

x=-6

NO SOLUTION

400

log(5x+14)=log(7x-2)

x=8

500

(log₂(6x-8))/log₂x=2

x= 4

x=2

SOLVING LOGARITHMIC/EXPONENTIAL EQUATIONS

100

log x + log(x+3) = 1

x= -5 extraneous

x= 2 

200

6^x=8

ln8 / ln6 aprox. 1.606

300

e^3.5t=42

t= ln42/3.5 

aprox. 1.0679

400

5^x-2=3^x

2log5 / log5-log3

500

(log(3x-4))/log x = 2

no solution

SOLVING SYSTEMS OF LINEAR EQUATIONS

100

Solve using elimination or substitution

y=-5x -2

y+2=-5x

infinitely many solutions

200

Solve:

y=6x+2

3y-18x=12

6=12

no solution

300

Solve:

2x+y+4z=12

x+2y+2z=9

3x-3y-2z=1

(3, 2, 1)

400

Solve:

4x-5y+5z=53

x-2y-z=8

2x-3y+z=23

0=0 

or ?

500

4/5x - y + z = 53/5

0.2x - 0.3y + 0.1z = 2.3

x - 2y - z = 8

0=0

REVIEW

100

What is the discriminant?

b²-4ac

200

How many solutions for the following:

1) discriminant >0

2) discriminant <0

3) discriminant = 0

1) two solutions

2) no real solutions

3) 1 solution

300

Find inverse of 

f(x)= (2x+1) / x-1

y=(x+1)/(x+2)

400

What type of asymptote does an exponential function have?

Which one is exponential? y=b^x   or   y=log_bx

Which is a point on the exponential parent graph?

(0,1) or (1,0)

horizontal y=0

b^x

(0,1)

500

Given f(x)=2x-6 and g(x)= 1/(x²+4)

Find (g o f)(3)

1/4

Review

100

How many solutions for the following:

1) discriminant >0

2) discriminant <0

3) discriminant = 0

1) two solutions

2) no real solutiona

3) 1 solution

200

Is the absolute value parent graph a one to one function?

Is the following a one to one function?

f(x)=6x-4

No

Yes

300

Find inverse of f(x)=x³-4

Find inverse of f(x)=(x+10)³

y=(x+4)^1/3

y= x^1/3 -10

400

Find inverse of the following:

f(x)= 2/3x -2

y= 3/2x +3

500

Find vertex of 

f(x)=-x²-4x-7

V(-2, -3)