Question

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Answer 1

Useful Log Rules:

• log(A*B) = log(A)+log(B)  .......... log rule 1
• log(A/B) = log(A) - log(B) .......... log rule 2
• log(A^B) = B*log(A)  ................... log rule 3

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Part (a)

All logs shown below are base 3.

log(500) = log(5*100)

log(500) = log(5*10^2)

log(500) = log(5)+log(10^2) .... use log rule 1

log(500) = log(5) + 2*log(10) .... use log rule 3

log(500) = 1.4650 + 2*2.096 ....... substitution

log(500) = 5.657

Answer: 5.657

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Part (b)

All logs shown below are base 3.

log(2) = log(10/5)

log(2) = log(10) - log(5) .... use log rule 2

log(2) = 2.096 - 1.4650  ....... substitution

log(2) = 0.631

Answer: 0.631