Online Course Discussion Forum
How to solve P12 from day 3 of the first week (logarithms)?
How do we solve P12 from day 3 of the first week? We didn't get to go over this one in classes.
Here's a few hints to get started. If you still get stuck, let us know and we can provide an additional thought.
Notice the similarities of the expressions inside the logarithms on the left hand side of each equation. First rewrite all the equations to remove this outside logarithm.
Then consider what happens when all those three equations are added together. Try to solve for the quantity $pqr$ first.
Hope this helps a bit!
Thanks for the tips, I previously got to that part but didn't really know how to proceed to solve for pqr since the equation I got from adding had both a pqr and a log pqr. Any hints on this?
Thinking of $pqr$ as a single variable, say $x$, the function you get should be an increasing function. Hence it should have a unique solution for $x = pqr$. With this in mind, you know that any solution you find must be the only solution. (Finding that one solution shouldn't be too hard.)
With a value of $pqr$, you should be able to then solve separately for $p$, $q$, and $r$.
Thanks, I solved the problem. I got u=3^(734-3u) where u=pqr and was able to find the pretty easily answer by inspection, but I was wondering if there was another way to find pqr that would work in general to solve equations with both a u and a log(u).
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