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Can someone please answer this?!?!?!
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\[31\log_{11} 5+\log_{11} 7\]
We'll use two important properties of Logarithms \[1) a\log_b c=\log_b c^a\] \[2) \log_c a+\log_c b= \log_c ab\] we have \[31\log_{11} 5+\log_{11} 7\] Using first property \[\log_{11} {5}^31+\log_{11} 7\] Using second property \[\log_{11} {{5}^31\time 7}\]
\[\log_{11} {5}^{31}+\log_{11} 7\] Using second \[\log_{11} {{5}^{31}\times 7}\]
So which one is the answer aahah?
The answer is \[\log_{11} (5^{31} \times 7)\]
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\[(31*\frac{\log5}{\log11})+(\frac{\log7}{\log11})\]
(31*20.80681999)+(0.811507563) the rest is your
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