Question

find instantaneous rate of change for function f(x)= log x, when x = 2.

Answer 1

the answer is not 1/2.

Answer 2

what's the answer given

Answer 3

is it log to the base 10 or e

Answer 4

log base 10

Answer 5

?

Answer 6

then change base first , we know that
\[\log_{a} x= \log_{e} x/\log_{e} a\]
so here
\[\log_{10} x=\log_{e} x/\log_{e} 10\]
so
\[f(x)=\log_{e} x/\log_{e} 10\]
now find f'(x)
which is
\[f'(x)=1/(x*\log_{e} 10)\]
x=2
so
\[f'(2)=1/(2*\log_{e} 10)\]
\[\log_{e} 10=2.302\]
\[f'(2)=1/(2*2.302)\]
\[f'(2)=0.2172\]