How do I condense each expression?
1 answer:
Answer:
![\log_5{\dfrac{x^5}{\sqrt[4]{8-x}}}](https://tex.z-dn.net/?f=%5Clog_5%7B%5Cdfrac%7Bx%5E5%7D%7B%5Csqrt%5B4%5D%7B8-x%7D%7D%7D)
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}}}](https://tex.z-dn.net/?f=5%5Clog_5%7Bx%7D-%5Cdfrac%7B1%7D%7B4%7D%5Clog_5%7B%288-x%29%7D%3D%5Clog_5%7Bx%5E5%7D-%5Clog_5%7B%5Csqrt%5B4%5D%7B8-x%7D%7D%3D%5Clog_5%7B%5Cdfrac%7Bx%5E5%7D%7B%5Csqrt%5B4%5D%7B8-x%7D%7D%7D)
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