# Find the derivative of y = log_10(x)

We define log functions as the inverses of exponentials.

## Answer: The derivative of log\(_{10}\)(x) = 1/ (x ln 10)

Let see, how we can find the derivative of y = log\(_{10}\)(x).

**Explanation: **

We have to find the derivative of log_{10} x

y = ln(x) ⇔ x=e^{y}

y = log\(_{10}\)(x) ⇔ x = 10^{y}

We will use the implicit differentiation to find the derivative of log\(_{a}\)(x).

d/dx [ln(x)] = 1/x

d/dx [log\(_{10}\)(x)] = 1 / (x ln 10). [Since log\(_{10}\)(x) = ln x/ln 10]

### Thus, the derivative of log\(_{10}\)(x) = 1/ (x ln 10).

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