Logarithms

Change form to exp

100

log₅1=0

5⁰ = 1

200

log₄4=1

4¹ = 4

300

log₂2⁷=7

2⁷ = 2⁷

400

log_a x = b

a^b = x

500

log_m x^y = n

mⁿ = x^y

Conversion to log

100

3³=9

log₃9=3

200

10^x=2

log2=x

300

4^x=20

log₄20=x

400

10²=3x+4

log(3x+4)=2

500

10^15x=3⁴

log 3⁴=15x

Name the law

100

log₂3 + log₂5

Multiplication law

200

log₃8 - log₃4

Division law

300

2log₅10

Power law

400

4log₂9 - log₂3

Power law and division law

500

2log₃8 + log₃6 - log₃12

Power law, Multiplication law, Division law

Expansion

100

log(x)³

3 log(x)

200

log(ab)^1/2

1/2 log(a) + 1/2 log(b)

300

log(x⁴ / 2)

4 log(x) - log(2)

400

log(x(y/z)^1/2)

log(x) +1/2 log(y) - 1/2log(z)

500

log(r^1/3/3s)

1/3 log(r) - log(3s)

Make as single log

100

log(3) + log(x)

log(3x)

200

3 log₂(4) + 3 log₂(x) + 3 log₂(y)

log₂(4xy)³

300

2 log₄(x) - y log₄(3)

log₄(x²/3^y)

400

2 log₃(x) + log₃(z) +2 log₃(y)

log₃((x²z)/y²)

500

3 log₄(z) + 2 log₄(x) - 5 log₄(y)

log₄((z³x²)/y⁵)