Problem

Translate the logarithmic statement into an equivalent exponential statement.
\[
\log 0.01=-2
\]

Answer

Expert–verified
Hide Steps
Answer

Final Answer: The equivalent exponential statement of the logarithmic statement \(\log 0.01=-2\) is \(\boxed{10^{-2} = 0.01}\).

Steps

Step 1 :Translate the logarithmic statement into an equivalent exponential statement: \(\log 0.01=-2\).

Step 2 :The logarithm base 10 of a number is the exponent to which 10 must be raised to get that number. So, in this case, the base is 10, the exponent is -2, and the number is 0.01.

Step 3 :Therefore, the equivalent exponential statement is \(10^{-2} = 0.01\).

Step 4 :Final Answer: The equivalent exponential statement of the logarithmic statement \(\log 0.01=-2\) is \(\boxed{10^{-2} = 0.01}\).

link_gpt