Exponential & Logarithm Functions

Transformations

100

f(x) = 5(2/3)^x

What is the transformation on the parent function?

Growth or decay?

Vertical stretch by 5

Decay

200

f(x) = 3^x + 2

What is the transformation on the parent function?

Growth or Decay?

Up 2

Growth

300

f(x) = 3^x+1 - 6

What is the transformation on the parent function?

Growth or Decay?

Left 1, down 6

Growth

400

f(x) = -(1/2)^x-5 + 2

What is the transformation on the parent function?

Growth or decay?

Reflection over x-axis, right 5, up 2

Decay

500

f(x) = 2(1/4)^x-1 - 3

What is the transformation on the parent function?

Growth or decay?

Vertical stretch by 2, right 1, down 3

Decay

Exponential Equations

100

Solve.

9^3x-7 = 9^5-x

x = 3

200

Solve.

8^6y+4 = 64

y = -1/3

300

Solve

8^x+2 = 4

x = -4/3

400

Solve.

16^r-2 = 64^r+2

r = -10

500

Solve.

(1/4)^2x = 32^4x-2

x = 5/12

Converting

100

Write in logarithmic form.

8² = 64

log₈64 = 2

200

Write in exponential form.

log₃27 = 3

3³ = 27

300

Write in logarithmic form.

2^x-4 = 32

log₂32 = x - 4

400

Write in exponential form.

log₄90 = x

4^x = 90

500

Write in logarithmic form.

10^2x = 54

log₁₀54 = 2x

Evaluating Logs

100

Evaluate logarithm.

log₆1

x = 0

200

Evaluate logarithm.

log₉81

x = 2

300

Evaluate logarithm.

log63

1.7993

400

Evaluate logarithm.

log₇95

2.3402

500

Evaluate logarithm.

log₂78

6.2854

Condensing & Expanding

100

Expand.

log₃(xy)

log₃ x + log₃ y  

200

Expand.

log₃(x/y)⁴

4log₃ x - 4log₃ y

300

Condense.

30log a + 6log b

log(b⁶a³⁰)

400

Expand.

log₇(a⁵/b)⁴

20log₇ a - 4log₇ b

500

Condense.

3log2 + log(x - 4)

log(8x - 32)