Question

How do I condense each expression?

Answer 1

Answer:

  $\log_5{\dfrac{x^5}{\sqrt[4]{8-x}}}$

Step-by-step explanation:

Make use of the rules of logarithms:

  log(a/b) = log(a) - log(b)

  log(a^b) = b·log(a)

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  $5\log_5{x}-\dfrac{1}{4}\log_5{(8-x)}=\log_5{x^5}-\log_5{\sqrt[4]{8-x}}=\log_5{\dfrac{x^5}{\sqrt[4]{8-x}}}$