Logs and Exponentials!

Expand

100

log₂x/y

log₂x - log₂y

200

log₆(xy³)

log₆x + 3log₆y

300

log₅(uv³)⁴

4log₅u + 12log₅v

400

log₄(3⁴/7)⁶

24log₄3 - 6log₄7

500

log₃((zx)⁶/y)²

12log₃z +12log₃x - 2log₃y

Condense

100

logx + logy

log(xy)

200

log₂3 + 4log₂y

log₂3y⁴

300

5lnx - 12lny

ln(x⁵/y¹²)

400

9log₅x + 3log₅y + 3log₅z

log₅(x⁹y³z³)

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 initial population of foxes in 2004. 

200

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

A 6% population decrease.

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. 

y = 525(1.012)^t

400

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

$1742.75

500

$2000 is invested into an account that earns 5% interest compounded quarterly. Find the balance after 3 years.

$2321.51

Solve Exponentials

100

4^-x = 4³

x = -3

200

14^x = 88

x = 1.70

300

16^-2x+2 = 8^x-2

14/11 or 1.27

400

20⁶ⁿ⁺⁷ + 2 = 87

-0.92

500

8(4^9-5x)+1 = 3

x = 2