Logarithms

Evaluating Logarithms Without a Calculator

100

log₂(4)

2

200

log₅(625)

4

300

What is the capital of New York?

Albany

400

log₂(1)

0

500

log(1000)

3

Condense Into a Single Logarithm

100

3 log₆(m) - 1/2 log₆(n)

log₆(m³/sqrt(n))

200

log(3) + log(20) - log(4)

log(15)

300

log₃(x) + log₃(x-4)

log₃(x² - 4x)

400

3 log₇(x²) + 4 log₇(y³)

log₇(x⁶y¹²)

500

5 log(m) - log(m²)

log(m³)

Solving Equations:Log = Log

100

log₇(9x-4) = log₇(x+20)

x = 3

200

log₅(m² - 12) = log₅(m)

m = 4

300

log₁₄(x²+2x) = log₁₄(40-x)

x = -8, x = 5

400

log(2y - 10) = 7 log(2) - log(8)

y = 13

500

What is the biggest of the great lakes?

Lake Superior

Solving Equations:Log = Number

100

log₄(5m+9) = 3

m = 11

200

log₃₆(20-4p) = 1/2

p = 7/2 or 3.5

300

log₆(9) + log₆(4x²) = 4

x = 6, x = -6

400

log₃(x+6) - log₃(x) = 2

x =3/4

500

log₄(x) - log₄(x+5) = 1

No Solution

Solving Equations:Exponential

100

25^(v-2) = 625

v = 4

200

Free Points!

+200

300

216^(-2x-2) = 36^(-2x)

x = -3

400

Who is on the $10 bill?

Alexander Hamilton 

500

5^(2x) . 625 = 25

x = -1