# Differentiating Logarithmic Functions without Base e

In mathematics, the study of logarithmic functions is essential for understanding various phenomena, from exponential growth to complex systems. While the natural logarithm with base 'e' is widely known and utilized, exploring logarithmic functions with different bases unveils intriguing insights and applications. This introduction aims to delve into the differentiation of logarithmic functions without base 'e', shedding light on the fundamental principles and techniques involved. By examining alternative bases for logarithms, we can expand our understanding of mathematical operations and their practical implications in diverse fields such as finance, engineering, and science.

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- What is the derivative of #log_3((xsqrt(x-1))/2)#?
- How do you differentiate #y = log_2 (x^4sinx)#?
- How do you differentiate #log(8x-1)#?
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- How do you find the derivative of #e^(x*log(x))#?