Question

How do you solve `-2=log_x (1/100)`?

Answer 1

`x= 10`

Explanation:

`-2 = log_x (1/100)`

There are many ways you can solve this problem. The best approach is to convert the given equation to exponent form.

Rule : `log_b (a) = k => a= k^b`

Using the rule we can get

`x^-2 = 1/100`
`x^-2 =1/10^2`
`x^-2 = 10^-2` Rule `1/a^m = a^-m`

`x= 10` The final answer.

Alternate approach

`-2 = log_x (1/100)`
`-2 = log_x (10^-2)`
`-2 = -2 log_x (10)` Rule `log(A)^n = n log(A)`
`1 = log_x (10)`
`x =10` because of the rule `log_a (a) = 1` x has to be 10.