Question

Write the following equation in its equivalent logarithmic form.
RootIndex 4 StartRoot 16 EndRoot equals 2
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Part 1
The equation in logarithmic form is
  
enter your response here.
​(Type an​ equation.)

Answer 1

To write the equation \( \sqrt[4]{16} = 2 \) in its equivalent logarithmic form, we start with the general relationship between exponents and logarithms.

The expression \( \sqrt[4]{16} \) can be written as \( 16^{1/4} \), and we denote the equation as follows:

If \( b^y = x \), then the logarithmic form is \( \log_b(x) = y \).

In this case:

- \( b = 4 \) (the index of the root)
- \( x = 16 \) (the number under the root)
- \( y = 2 \) (the result)

Thus, we can write it in logarithmic form as:

\[
\log_4{16} = 2
\]

So, the equation in logarithmic form is:

\[
\log_4{16} = 2
\]