0.2 <= logx < 2
take the antilog of each side..
100.2 < x < 10^2
To solve the inequality 0.2 <= log(x) < 2, we need to take the antilog of each side in order to isolate x.
An antilog, or exponentiation, is the inverse operation of a logarithm. It helps us "undo" the logarithm and find the original value.
To find the antilog of a logarithmic expression, we raise the base of the logarithm to the power of the expression. In this case, the base is 10.
So, taking the antilog of the inequality, we have:
10^0.2 <= 10^(log(x)) < 10^2
10^0.2 is approximately equal to 1.585, and 10^2 is equal to 100.
Therefore, the inequality becomes:
1.585 <= x < 100
This means that x must be greater than or equal to 1.585 and less than 100 in order for the inequality to be true.