Question

How do I find the derivative of `(x)=Log_5(x)`?

Answer 1

`d/dx log_5(x) = 1/(xln(5)) = log_5(e)/x`

Explanation:

Recall from logarithmic properties that `log_5(x) = ln(x)/ln(5)`

Thus `d/dx log_5(x) = d/dx ln(x)/ln(5)`

Since `1/ln(5)` is a constant,

`d/dx ln(x)/ln(5) = 1/ln(5) d/dx ln(x) = 1/ln(5) * 1/x = 1/(xln5)`

You can also use the fact that `1/ln5 = log_5(e)` to present the answer differently

`d/dx log_5(x) = 1/(xln5) = log_5(e)/x`