Question

derivative of log x to the base 5 with respect to log 5 to the base x is​

Answer 1

Answer:

The derivative of log5(x) log 5 ( x ) with respect to x is 1xln(5) 1 x ln ( 5 )

Answer 2

Step-by-step explanation:

Simple. Let y = log(x^5), clearly x is not zero . Now, if the base of the logarithm is e , then y = ln(x^5) ==> dy/dx = y’ = 5.x^4/x^5 = 5/x .

But if base is a > 1, then y = log(x^5) = ln(x^5)/ln(a) ==> dy/dx = y’=(1/ln(a)).(5/x) = 5/(x.ln(a)) .