Question

If logx=-2, what is x?
A. 0.02
B. 0.01
C. -0.02
D. -0.01

Answer 1

\[\quad\log_b x = y\\\qquad\quad\Updownarrow\\\qquad x =b^y\]

Answer 2

When the base isn't specified it usually means base ten
\[\log = \log_{10}\]

Answer 3

so whenever you have a log function, the base 10 is implied.

essentially, the log function tells you 10 to the what power equals your input number.

Ex: 10^2 = 10*10 = 100. so log(100) = log(10^2) = 2
Ex2: 10^-1 = 1/10 = 0.1 so log(0.1)=log(10^-1)=-1

In your case, the output of the log function is -2. So to find x, you just have to put -2 as the exponent of 10.

10^-1 = 1/(10*10) = 1/100=0.01

Alternately, you can think of the log function as the inverse of 10^x and vice versa.
If you have the inverse of numbers, you can use them to cancel each other out
like 1/2*2 = 1

To cancel the log function out, you need to put 10 to the power of both sides of the equation (that way the equation stays balanced)