Algebra 2 Review

Trivia

100

What part of the exponential form is the logarithm?

The exponent

200

What is the exponential form?

b^x = y

300

What is the logarithmic form?

y = log_bx

400

How does the base of an exponential equation compare to the base of the related logarithmic equation?

They are the same

500

What is Mrs. Renze's favorite NFL team?

MN Vikings

Log to Exponential Form

100

log₃81 = 4

3⁴ = 81

200

log_x100 = 2

x² = 100

300

log₄16 = 2

4² = 16

400

log₂₇X = 2/3

27^2/3 = x

500

log₅Y = 2

5² = Y

Sequences

100

Is the following sequence arithmetic or geometric?

1, 3, 9, 27, ...

Geometric

200

How do you tell if a sequence is arithmetic vs geometric?

Arithmetic deal with addition or subtraction, geometric deal with multiplying and dividing.

300

What is the recursive formula for an arithmetic sequence? 

a_n = a_n-1 + d

400

What is the explicit formula for a geometric sequence?

a_n = a₁(r)^n-1

500

what is the 27th term of this sequence?

3, 6, 9, 12,....

7.62559748E12

Exponential to Log form

100

27 = 3^x

log₃ 27 = x

200

3² = 9

log₃ 9 = 2

300

5³ =125

log₅ 125 = 3

400

e^a = b

log_e b =a

500

10¹ = 10

log₁₀ 10 = 1

Evaluate Expressions

100

log₃ X = 4

X = 81

200

log₂₅ 5 = X

X = 1/2

300

log_x 4 = 1/2 

X= 16

400

log_1/2 128 = y

y = -7

500

log_1/3 (1/81) =x

x= 4