Properties of logarithms

Product rule

100

oh ohh

You lost a turn! And lost your money!

200

log_b(MN)

log_b(M)+log_b(N)

300

Give an example of when to use the product rule.

Log₆ 36 * 216

log4 16x

400

log_b(8k)

log_b 8 + log_b k

Quotient rule

100

log_b(NM)

log_b(M)−log_b(N)

200

Sorry! Try again!

You get to keep your money for another turn. 

300

log (2x/3)

log 2x - log 3

log 2 + log x - log 3

400

You lost your turn! 

You also lost your money!

Power rule

100

log_b (x²)

2* log_b x

200

log_b(2⁸)

8 * log_b 2

300

Wrong choice! No questions here!

Better luck next time! You lost your money and your turn!

400

log_b (Mⁿ)

N * log_b M

Equality rule

100

Solve 2logb(x) = logb(4) + logb(x – 1)

2logb(x) = logb(4) + logb(x – 1)

logb(x2) = logb((4)(x – 1))

logb(x2) = logb(4x – 4)

x2 = 4x – 4

x2 – 4x + 4 = 0

(x – 2)(x – 2) = 0

Hence the solution is:

x = 2

200

No questions

Try again

300

Log_b u = Log_b v

U=V

400

Pretty close

But not close enough