Question

How do I condense each expression?

Answer 1

`\log_5{\frac{x^5}{\sqrt[4]{8-x}}}`

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}-(1)/(4)\log_5{(8-x)}=\log_5{x^5}-\log_5{\sqrt[4]{8-x}}=\log_5{\frac{x^5}{\sqrt[4]{8-x}}}`