Question

derivative :
y=logx
@zepdrix

Answer 1

The `Natural Log` is the log that we can easily find a derivative of.
Since this log has no base labeled, it's by default a log base 10.

We'll need to change the base of this log, using rules of logarithms.\[\large \log_a(b)=\frac{\log_c(b)}{\log_c(a)}\]
Using this rule, we can change our log from base \(a\) to base \(c\), where \(c\) is anything we want it to be.

Answer 2

\[\large \log (x) \qquad = \qquad \log_{10}(x) \qquad = \qquad \frac{\log_e(x)}{\log_e(10)}\]So we used the rule to change the base to a base of \(e\), which is the natural log, so we can write it like this.\[\large y=\frac{\ln x}{\ln 10}\]

Answer 3

Again we think of that invisible 1 being there ;) and pull out the ugly denominator.\[\large y=\left(\frac{1}{\ln 10}\right)\ln x\]

Answer 4

1/ln10 is just a constant, we can ignore it while we take the derivative.
Just take the derivative of the ln x portion.
Do you remember that derivative? :)

Answer 5

ill put x in the deno.?

Answer 6

1/ln10x?

Answer 7

yes good, the derivative of \(\ln x\) is \(\dfrac{1}{x}\).

Which gives your answer.

Answer 8

you might want to write it like 1/ln(10)x so it's clear that the x is NOT inside of the log. It's not connected to the 10.

Answer 9

aight. thank u very much!;)