Logarithms Review!!!

General Log questions

100

The exponential form of this is what?

 log_bx = y

b^y = x

200

Write the Expression in exponent form

log₃27 = 3

3³ = 27

300

Write the Expression in exponent form

Log₉27 = 2/3

9^2/3 = 27

400

Q1. Write the Expression in Logarithmic form.

 2^-4 = 1/16

Q2: What is the base of the following?

log(x)

Log₂1/16= -4

10

500

Write the equation in logarithmic form

8^4/3 = 16

Log₈16=4/3

Converting/ Evaluating

100

Evaluate. Use the Change of base formula if needed

Log₂32

2^x = 32

x = 5

200

Convert to exponential form (no solving):

log_1/3 (x + 2) = 4

1/3⁴ = x + 2

300

Evaluate. Use change base formula when necessary

log₁₆8

log8   =  .75

log16 

400

Evaluate: 

log₆1/36

-2

500

32^{x + 6} * 1/2 = 8^{x - 1}

32^{x + 6} * 1/2 = 8^{x - 1}

2^{5(x + 6)} * 2^-1 =2^{3 (x - 1)}

2^{5x + 30} * 2^-1 = 2^{3x - 3}

5x + 29 = 3x -3

2x = - 32   Therefore, x =-16

Solving Exponential Eq Using Common base

100

4^(2x-1)=64

x=2

or

(log_4(64)+1)/2

200

32^(x-2)=64

x=log_32(64)+2

300

5*2^{x +10} =40

x = log₂6

2^{x + 10} = 8

2^{x + 10} =2³

x + 10 = 3

x = -7

400

log₃(x - 3) = 2

3²= x - 3

x = 12

or 

3^2 + 3 = 12

500

Evaluate. Use change base formula when necessary

Log₅38

log38  = 2.2602

log5

Graphing logs

100

What is the range of every logarithmic function?

All real numbers

or

(-infinity, infinity)

200

Identify the vertical and horizontal shift of the following logarithmic function: 

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

2 to the left and 1 up

300

What is an asymptote?

A line that a function approaches but never touches

400

What would be the asymptote for the following function?

log(x-5)+2

x=5

500

Find: Domain, Range, As x--> __, f(x) -->__, 

x intercept & asymptote   , 

f(x)= -3log_2x

Domain: x > 0 

Range: All REAL Numbers

As x--> Infinity f(x) --> (-) infinity 

x intercept (1, 0)

asymptote x = 0

Properties of Logs

100

log₆ 3² in its expanded form?

What is 2log₆ 3

200

7log₄ X + 4log₄ Y in its condensed form?

What is log₄ ( X^{7 .} Y⁴)

300

5log₇ w + 5log₇ u + 15log₇ v in its condensed form?

What is log₇(w^{5 .} u^{5 .} v¹⁵)

400

5log₉ u - 12log₉ v in its condensed form?

What is log₉ u⁵/v¹²

500

log₇ ((a ^. b)⁵/c)⁴ in its expanded form?

What is 20log₇ a + 20log₇ b - 4log₇ c