Question

Write in logarithmic form.
StartFraction 1 Over 25 EndFraction equals 5 Superscript negative 2
Question content area bottom
Part 1
The logarithmic form is
  
enter your response here.
​(Use integers or fractions for any numbers in the​ expression.)

Answer 1

To convert the equation \( \frac{1}{25} = 5^{-2} \) into logarithmic form, we identify the base, the result, and the exponent.

The logarithmic form of \( a^b = c \) is written as \( \log_a(c) = b \).

In this problem:

- The base \( a \) is \( 5 \)
- The result \( c \) is \( \frac{1}{25} \)
- The exponent \( b \) is \( -2 \)

So we can write:

\[
\log_5\left(\frac{1}{25}\right) = -2
\]

Thus, the logarithmic form is:

\[
\log_5\left(\frac{1}{25}\right) = -2
\]