Logarithms Review (jd)(No Calculator)

1. Converting Log and Exponential Form AND Evaluating

100

Convert to Exponential Form:

log_2(8)=x

2^x=8

200

Solve Using Logarithms:

log_3(1/27)=

x= -3

300

Convert to Exponential Form:

log_(x)(4)=2y

(x)^(2y)=4

400

Solve using Logarithms:

 

log_x(1/64) = -2

 x = 8

500

Convert to Exponential Form:

log_(3)(5-z)=4y

(3)^(4y)=5-z

2. Solving Exponential Equations with Log Properties

100

Solve for x:

5^(2x)=25

x=1

200

Solve for x:

5*2^x=240

log_(2)(48)

300

Solve for x:

3^(2x)=27

x=3/2

400

Solve for x:

2*3^(x-5)=12

log_(3)(6)+5

500

Solve for x:

 2^(3x)-7=13

(log_(2)(20))/3

3. Expanding/Condensing Logarithms

100

Condense the Logarithms:

log_3(2x)-log_3(5y)

log_3((2x)/(5y))

200

Completely Expand the Logarithm:

log((2x)/y)

log(2)+log(x)-log(y)

300

Condense the Logarithms:(use ln the same as any other log)

2log(3)-2log(x)+4log(y)

log((9y^4)/x^2)

400

Condense the Logarithms:

3log(x)+4log(2)-5log(z)+3log(3)

log((16x^3)/(27z^5))

500

Completely Expand the Logarithm:

log_7((3x^6y^7)/(z^5))

log_7(3)+6log_7(x)+7log_7(y)-5log_7(z)

4. Miscellaneous Challenges

100

Write 1 as log base 2.

What is log₂2 ?

200

Write 2 as a natural log.

what is 2lne or lne^{2 ?}

300

Simplify into 1 log:

2Ln5 + 2

ln(25/e²)

400

Given: y = log₂x,

write log₂x² in terms of y.

2y

500

Given: p = log_a4  and  q = log_a5 , 

write log_a100 in terms of p and q

p + 2q

5. More Solving Equations

100

log₃x+log₃6=2

What is 1.5?

200

log₂x+log₂(x-2)=3

What is 4? (not -2)

300

16log₂x + 4log₄x = 36

what is 4?

400

Solve

log₅(2x-7)=log₅(3x-9)

What is no solution?

500

Solve

log_(1/2)8 + log₂(1/8) = x

what is -6 ?