Asked by Jon

Evaluate log(6)√6 (actual question)

There's a problem in my book that says:

Convert each logarithm to a natural logarithm and evaluate log(5)√288
the answer in the back is 1.7593 but I can't find an example of those kinds.
Answered by Reiny
your book should show two of several important properties of logs
1. log<sub>a</sub> a = 1
2. log<sub>a</sub> b = log<sub>10</sub> a/log<sub>10</sub> b

in log(5)√288 they used #2 rules
log(5)√288
= log(√288)/log 5
= log(16.97056275)/log5
= 1.22969244/.69897 1.759297

for the first of your questions we don't even have to use that

log<sub>6</sub> √6
= (1/2)log<sub>6</sub> 6
= (1/2)(1)
= 1/2
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