Question 4709
I'll answer the first two of your questions, but I can't seem to get the graph to work for logarithms.  I have tried and tried, and I can't make it work.  Maybe Igor will help us out with this one. 


Question 1.  
You are correct! {{{log (x, 5) = 1/3}}} changed to exponential form becomes {{{x^(1/3) = 5}}}.  To solve this just cube both sides, giving you {{{x = 5^3 = 125}}}


Question 2.  
{{{3lnx^2 + ln(2x-4)-ln(3x-6)}}}
{{{6ln (x) + ln (2x-4) - ln(3x-6)}}}
{{{6 ln (x) + ln ((2x-4)/(3x-6)) }}}
{{{6 ln(x) + ln ((2(x-2)) /(3(x-2))) }}}
{{{6 ln(x) + ln (2/3) }}}, for all values of x but x cannot equal 2.

Question 3.

My best shot, but it doesn't seem to work:

{{{ graph (400, 400, .5, 10, -10, 10, (log(e,x))/(log(e,4)) ) }}}

Stumped me on this one.  Maybe someone else can help us out.  Sorry.


R^2 at SCC