Nadira Nadira
  • 09-06-2025
  • Mathematics
High School

find the exact value of log_5(root(5, 3))

Show all work please

find the exact value of log 5 root 5 3 Show all work please

Answer :

mhanifa mhanifa
  • 16-09-2024

Answer:

  • [tex]\cfrac{1}{3}[/tex]

-------------------------------

Given:

  • [tex]log_5\sqrt[3]{5}[/tex]

Find its exact value:

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

Used properties:

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