Question

Find the exact value of the logarithmic expression without a calculator. Show all work

log3 4√27

Answer 1

3/4 or 0.75

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Given expression

• 
  `log_3\ \sqrt[4]{27}`

Find its value using logarithm rules:

• 
  `log_3\ \sqrt[4]{27} =log_3\ \sqrt[4]{3^3} =log_3\ 3^(3/4)=3/4\ log_3\ 3=3/4`

The rules used above:

• 
  `log_a\ a=1,\ log_a\ b^c=c\ log_a\ b`