Question

Find the exact value of log_5(root(5, 3))
Show all work please

Answer 1

• 
  `\cfrac{1}{3}`

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Given:

• 
  `log_5\sqrt[3]{5}`

Find its exact value:

• 
  `log_5\sqrt[3]{5} =log_55^(1/3) =\cfrac{1}{3} \ log_55 = \cfrac{1}{3} *1=\cfrac{1}{3}`

Used properties:

• 
  `log_aa = 1, \ log_ab^c=c\log_ab,\ \sqrt[n]{a}=a^(1/n)`