Logs Logs Logs

Log Properties

100

2log3 - log8

log (9/8)

200

3ln2 + 5ln2 - ln3

ln (256/3)

300

1/2log(4) + log(2xy)

log(4xy)

400

2log₅(5x) + log₅y - log₅(x+1)

log₅(25x²y/x+1)

500

5(log2x - logy) - (log3 + 2log5)

log(32x⁵/75y⁵)

Solving Case 1

100

log₅(5x+7) - log₅(8) = log₅(49)

x=77

200

log₅(x-8) - log₅(2) = log₅(78)

x=164

300

log(2+x) - log(x-2) = log(3)

x=4

400

log₂(x+8) - log₂(3-x) = log₂(10)

x=2

500

log₄(x+1) - log₄(7) = log₄(2x-3)-log₄(3)

x=24/11

Solving Case 2

100

log₄(-4x) - log₄(6) = 1

x=-6

200

log₈(5) + log₈(5x-1) = 2

x=69/25

300

log₅(2) + log₅(x+7) = 1

x= -9/2

400

log(x-3) - log(x) = 2

x= -1/33

500

log₃(x+4) - log₃(x-4) = 3

x= 56/13

Solving Case 3

100

4^2x-1 = 64

x=2

200

32^x-2 = 64

x= log₃₂64 + 2

x= 3.2

300

3^x - 12 = 11

x= log₃23

x= 2.85

400

5*2^x +10 = 40

x= log₂6

x= 2.58

500

5 - 4^x *2 = -17

x= log₄11

x= 1.73

General Knowledge

100

Which five colours make up the Olympic rings?

Black, green, blue, yellow and red

200

What is the capital city of Finland?

Helsinki

300

What nut is in the middle of a Ferrero Rocher?

Hazelnut

400

Where is known as ‘the happiest place on Earth?’

Disneyland

500

How far is the Earth from the Sun?

149.63 million km