LOGARITHMS

Name Which Rule

100

log(100) + log(1000)

Green Rule

200

log₆(216) - log₆(36)

Yellow Rule

300

log₃(81) = log(81) / log(3)

Blue Rule

400

7^x = y  <-----> log₇(y) = x

Red Rule

500

log₄(16) = 2 * log₄(4)

Purple Rule

Green Rule

100

log(10) + log(10)

log(100) = 2

200

log₂(4) + log₂(8)

log₂(32) = 5

300

log₄(64) + log₄(4)

log₄(256) = 4

400

log₇(49) + log₇(x)

log₇(49x)

500

log₂(4x) + log₂(2/x)

log₂(8) = 3

Yellow Rule

100

log(10) - log(10)

log(10/10) = log(1)

200

 log₂(8) - log₂(4)

log₂(8/4) = log₂(2) = 1

300

log₄(64) - log₄(4)

log₄(64/4) = log₄(16) = 2

400

log₇(343) - log₇(7)

log₇(343/7) = log₇(49) = 2

500

log₂(16/x) - log₂(2/x)

log₂((16/x) / (2/x)) = log₂(16/2) = log₂(8) = 3

Blue Rule

100

log₂(8)

log₁₀(8) / log₁₀(2) = 3

200

log₃(243)

log₁₀(243)/log₁₀(3) = 5

300

log₅(125)

log₁₀(125) / log₁₀(5) = 3

400

log₇(343)

log₁₀(343)/log₁₀(7) = 3

500

log₉(6561)

log₁₀(6561)/log₁₀(9)

Purple Rule

100

log₂(2⁷)

7 * log₂(2) = 7

200

log₃(9⁵)

5*log₃(9) = 10

300

log₅(25⁷)

7*log₅(25) = 14

400

log₄(64⁸)

8*log₄(64) = 24

500

log₈(512⁴)

4*log₈(512) = 12