LOGS

Exponential Equations

100

Solve:

3^3x-2=27

x=5/3

200

216 * 6^x+3=1

x=-6

300

64^1-3x / 16 = (1/64)^x

x=1/6

400

25^{x^2+x+1} * (1/5)^{x^2-x} = 1

x = -1, -2

500

(8^2x+1) / (2^3x) = 4 * sqrt(32)

x=1/2

Evaluating Logs

100

log₂(16)

4

200

ln(e⁵)

5

300

log(1/100)

-2

400

log_2/3(9/4)

-2

500

ln(ln(ln(e^e)))

0

Log Properties

100

Rewrite as a single log:

3log(u)+4log(v)-2log(w)

log(u³v⁴/w²)

200

Expand:

log(z³ * sqrt(xy⁵))

3log(z) + (1/2)log(x) +(5/2)log(y)

300

Given: log(a)=10, log(b)=11, log(c)=-9

Evaluate:

log(b³c³/sqrt(a³))

-9

400

Evaluate:

log₄(27)/3 - log₄(6)

-1/2

500

Evaluate:

-log₃(32)/5 - log₃(54) + 2log₃(2)

-3

Log Equations

100

log(x+1)-log(x)=1

x=1/9

200

log₉(4x-1)=log₄(2)

x=1

300

log₄(x-2) + log₄(x-2)=0

x=3

400

log₄(log₉(log₂(x))) = -1/2

8

500

log₅(-4x) - 3log₅(2) + log₅(-x)=2

-5sqrt(2)

Random Trivia

100

What brand famously used the slogan "Taste the Rainbow?"

Skittles

200

What is the only letter that doesn't appear in any U.S. state name?

Q

300

What animal can hold its breath longer than a dolphin (up to 40 minutes) underwater?

Sloth

400

What is the only food that never spoils - like, literally lasts forever?

Honey

500

In what country is it illegal to own only one guinea pig because they get lonely?

Switzerland