# SOLUTION: express as a single log: 1/2loga x + 4loga y -1/3loga z

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 Click here to see ALL problems on Exponential-and-logarithmic-functions Question 107094: express as a single log: 1/2loga x + 4loga y -1/3loga zAnswer by solver91311(16897)   (Show Source): You can put this solution on YOUR website!Let's look at what we know about logarithms: , Using these facts, let's operate on your orignial expression: Beginning with the first term, remember that , so Similarly, the other two terms become: , and ( is the cube root of z, but I can't render that on this system) Putting the terms together, using the second rule from above: The answer would be much neater if I could replace the fractional power on z with a cube root radical, but it is still correct in this form.