Midterm Review

Logarithmic/Exponential Eq.

100

Solve 

log(2x)+ 3 = 4

x=5

200

log₂(3x-4) = 3

x=4

300

Solve

2 - log₇x = log₇(x-48)

x= 49

400

Solve

ln(x-4) = ln(x+6) - lnx

x= 6

x=-1 is no good

500

Solve

log₂(4x+10) = 3

x= -1/2

Logarithmic/Exponential Graphs

100

What are two points for the following function?

f(x)= 3^x

(0, 1)

(1, 3)

200

Describe translations. What is the asymptote? 

f(x)= 3^x-1 + 2

y=2

Move right one unit

Move up two units

300

Write in logarithmic form. 

12²=144

log₁₂ 144 = 2

400

What are two points on the following graph? What is the asymptote? What is the inverse function?

f(x)= log₂(x) 

(1, 0)

(2, 1)

x=0

f^-1(x)= 2^x

500

Describe translations of h(x).

What is the asymptote? 

h(x)= log₂(x+1) + 2

Move left one unit

Move up two units

x= -1

Review 1

100

Find vertex and a.o.s.

f(x)= -6x² +12 -1

(1, 5)

x=1

200

x - 5^1/2 +6=0

x=9

x=4

300

SOLVE SYSTEM

-5x - 4y = 2

4x + y = 5

(2, -3)

400

Given

f(x)= x²+2x and g(x)=x+2

Find (f o f)(3)

255

500

Given

f(x)= x²+2x     and     g(x)=x+2

Find (g o f)(3)

17

Review 2

100

Evaluate

log₇(1)=

ln(e)=

log₉(3)= 

0

1

1/2

200

Determine the number of solutions for the following

3x² -4x +3=0

2 imaginary solutions

or NO real solution

300

Solve 

5^x-2=7

x=ln7/ln5 + 2

400

Write as single log

1/2lnx + ln(x²+1) - ln(x+1)

ln ( x^1/2(x²+1) ) / (x+1)

500

Evaluate

4^2x+3=8^x

x= -6