The expression
`log_c(a) + log_a(b) + log_b(c)`
is equal to
- `1/(log_c(a)) + 1/(log_a(b)) + 1/(log_b(c))`
- `1/(log_a(c)) + 1/(log_b(a)) + 1/(log_c(b))`
- `-1/(log_a(b))-1/(log_b(c))-1/(log_c(a))`
- `1/(log_a(a)) + 1/(log_b(b)) + 1/(log_c(c))`
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The expression
`log_c(a) + log_a(b) + log_b(c)`
is equal to
`B`
`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(Let)\ \ x` | `=log_c(a)` |
`c^x` | `=a` |
`x log_a c` | `=log_a a` |
`x` | `=1/log_a c` |
`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)
`1.77\ \ text{(to 2 d.p.)}`
`log_3 7` | `= (log_10 7)/(log_10 3)` |
`= 1.771…` | |
`= 1.77\ \ text{(to 2 d.p.)}` |