smc-6455-30-Logs – COB Rule

L&E, 2ADV EQ-Bank 11

Evaluate \(\log _{3} 6\), giving your answer to 2 significant figures. (2 marks)

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\(\log _{3} 6=1.6 \ \text{(2 sig fig)}\)

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\(\log _{3} 6=\dfrac{\log _e 6}{\log _e 3}=1.6309 \ldots=1.6 \ \text{(2 sig fig)}\)

The expression

`log_c(a) + log_a(b) + log_b(c)`

is equal to

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`B`

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`text(Solution 1)`

`text(Using Change of Base:)`

`log_c(a) + log_a(b) + log_b(c)`

`=(log_a(a))/(log_a(c)) + (log_b(b))/(log_b(a)) + (log_c(c))/(log_c(b))`

`=1/(log_a(c)) + 1/(log_b(a)) + 1/(log_c(b))`

`=> B`

`text(Solution 2)`

`text(Apply similarly for the other terms.)`

`=> B`

Use the change of base formula to evaluate `log_3 7`, correct to two decimal places. (1 mark)

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`1.77\ \ text{(to 2 d.p.)}`

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