Question

How does a function look for f(x)=-2log3x. The 3 is below the x

Answer 1

if the function is \[f(x)=-2\log_{3}x \]then we can therefore write it as \[y=-\log_{\sqrt{3}}x \] which gives the general graph of a decreasing log function ie \[y=-\log_{a}x \] where a is a fraction...so we now see that when x=1 f(x)=0 and when x=0 f(x) is undefined (ie asymptote) , extra points on the graph can be\[\left( \sqrt{3};-1 \right) \left( 15 ;-4,9\right)\],see attached file

Answer 2

You can even write \[\log_{3}x \] as \[\ln x/\ln 3\].
Now the equation \[-2\log_{3} x\] becomes \[\left( -2/\ln 3 \right) \times \ln x\].
This can be plotted easily.

Answer 3

that is also a good approach, employing succinct problem solving techniques thanks

Answer 4

:-)