Question

Log 125/64 base 4/5 find ts value?

Answer 1

$</p><p></p><p> \sf \rightarrow \quad log_{ \frac{4}{5} } \: \frac{125}{64} \\ \\ \sf \rightarrow \quad log_{ \frac{4}{5} } \: 125 - log_{ \frac{4}{5} } \: 64 \\ \\ \sf \rightarrow \quad \frac{ log_{5} \: 125}{ log_{5} \: \frac{4}{5} } - \frac{ log_{4} \: 64 }{ log_{4} \: \frac{4}{5} } \\ \\ \sf \rightarrow \quad \frac{3}{ log_{5} \: 4 - log_{5} \: 5 } - \frac{3}{ log_{ 4 } \:4 - log_{4} \: 5 } \\ \\ \sf \rightarrow \quad \frac{3}{ log_{5} \: 4 - 1 } - \frac{3}{1 - log_{4} \: 5 } \\ \\ \sf \rightarrow \quad \frac{3 log_{4} \: 5 }{1 - log_{4} \: 5 } - \frac{3}{1 - log_{4} \: 5 } \\ \\ \sf \rightarrow \quad \frac{3 log_{4} \: 5 - 3 }{1 - log_{4} \: 5 } \\ \\ \sf \rightarrow \quad \frac{ - 3 \cancel{(1 - log_{4} \: 5) }}{ \cancel{(1 - log_{4} \: 5 )}} \\ \\ \sf \rightarrow \quad - 3</p><p>$

Answer 2

Answer:

$log_{\frac{4}{5} } \frac{125}{64} =-3$

Step-by-step explanation:

$log_{\frac{4}{5} } (\frac{125}{64} )\\\\=log_{\frac{4}{5} } (\frac{5}{4} )^{3} (log a^{n} =nlog a)\\\\=3log_{\frac{4}{5} } (\frac{5}{4} )\\ \\(log_{a} b= logb/loga) \\\\=3\frac{log_{\frac{5}{4} } }{log_{\frac{4}{5} } } \\ (log\frac{a}{b} =log a-log b)\\\\=3\frac{log5-log4}{log4-log5} \\\\=-3\frac{(log4-log5)}{(log4-log5)} \\\\=-3$

$log_{\frac{4}{5} }\frac{125}{64}$ =-3

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