Question

How do you evaluate `log_10(log_2[log_3 9])= x`?

Answer 1

`x = 0`

Explanation:

`If log_n x = a` Then `x = n^a`

In the question x is equal to a nest of log functions of different bases as follows:

`a = log_3 9`
`b = log_2 a`
`x = log_10 b`

Taking each in turn:

`a = log_3 9 = 2` Since `9 = 3^2`
`b = log_2 2 = 1` Since `2 = 2^1`
`x = log_10 1 = 0` Since `1 = 10^0`

Hence `x = 0`