Convert \(10^x = y\) to logarithmic form, step by step explanation.

To convert the equation \(10^x = y\) to logarithmic form, we need to identify the base of the exponent, which is 10 in this case.

The logarithmic form of the equation is:

\(\log_{10} y = x\)

Explanation:

1. The base of the exponent becomes the base of the logarithm.
2. The exponent becomes the result of the logarithm.
3. The result of the exponentiation becomes the argument of the logarithm.

Therefore, the logarithmic form of the equation \(10^x = y\) is \(\log_{10} y = x\).

Step 1: Take the logarithm of both sides of the equation \(10^x = y\) using base 10.

$$\log_{10}(10^x) = \log_{10}(y)$$

Step 2: Simplify the left-hand side using the property \(\log_{10}(10^a) = a\).

$$x = \log_{10}(y)$$

Therefore, the logarithmic form of \(10^x = y\) is:

$$\boxed{ \log_{10}(y) = x }$$