Logs and Exponentials!

Expand

100

log₂x/y

log₂x - log₂y

200

log₆(xy³)

log₆x + 3log₆y

300

log₅(uv³)⁴

4log₅u + 12log₅v

400

log₄ ((x²y³) / z²)

2log₄x +3log₄y - 2log_4z

500

Can you name the expand steps in order with the operations?

1.  Quotient (divide to subtract)

2.  Product (multiply to add)

3.  Power (exponent to coefficient)

Condense

100

logx + logy

log(xy)

200

log₂3 + 4log₂y

log₂3y⁴

300

5logx - 12logy

log(x⁵/y¹²)

400

Can you name the steps and operations for condensing logs?

1.  Power (coefficient to exponent)

2.  Product (add to multiply)

3.  Quotient (subtract to divide)

500

log₉x + 5log₉y - 6log₉z

log₉((xy⁵)/z⁶)

Solve Logs

100

log₁₇(-2x-1)=log₁₇17

-9

200

log₈x = 3

x = 512

300

7+log₃(x) = 11

x = 81

400

-7log(6-3n) = -7

-4/3 or -1.33

500

9log₉(2x - 9) + 6 = 24

x = 45

Growth/Decay/Interest

100

The population of foxes in a particular national park is modeled by equation, y = 215(0.94)^x, starting in 2004. What does 215 represent?

The number of foxes we started with.

200

The population of foxes in a particular national park is modeled by equation, y = 215(1.06)^x, starting in 2004. What does .06 represent?

A 6% population increase.

300

Maverick has a baseball collection valued at $525. The value increases by 1.2% annually. Create an equation that represents the value, y, of the collection after t years. 

Use y = A(1 +r)^t

y = 525(1.012)^t

400

$1500 is invested into an account that earns 5% interest compounded weekly. Find the balance after 3 years.

Use y = p(1 + r/n)^nt

$1742.63

500

$2000 is invested into an account that earns 6% interest compounded quarterly. How long will it take for the account to double in value?

12 years

Solve Exponentials

100

4^x = 4³

x = 3

200

14^x = 88

x = 1.70

300

16^-2x+2 = 8

.625 or 5/8

400

What is Mr. Harty's son's name?

Alex

500

8(4^-9-5x)+1 = 33

x = -2