Logarithms

Evaluating Logarithms

100

log₂(4)

2

200

log₅(625)

4

300

log₄(1/64)

-3

400

log₂(1)

0

500

log₄(1000)

4.9829

Condense Into a Single Logarithm

100

log₆(m) -  log₆(n)

log₆(m/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(x)- log₁₄(5) = log₁₄(24)

x = 120

400

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

y = 13

500

log₁₄(x²+2x) = log₁₄(40-x)

m = 4

Solving Equations:Log = Number

100

log₄(5m+9) = 3

m = 11

200

log₆(20)+log₆(p) = 2

p = 9/5

300

log₆(9) + log₆(4x²) = 4

x = 6, x = -6

400

log₃(6) - log₃(x) = 2

x =2/3

500

log₄(x) - log₄(x+5) = 1

No Solution

Solving Equations:Exponential

100

5^(v) = 625

v = 4

200

9^x = 25

x = 1.465

300

6^(3x) = 80

x = .8152

400

2^x+3 = 125

x = 3.9658

500

5.5^(x-2) = .3

x = 1.2938