Question

пожалуйста помогите с логарифмом
$1) \frac{ log_{25} 7}{ log_{625} } 2) \frac{9 log_{5}175^{9} }{ log_{5}7^{9} }$

Answer 1

2)
$\frac{9 log_{5}( {175}^{9} ) }{ log_{5}( {7}^{9} ) } = \frac{9 \times 9 log_{5}(175) }{9 \times log_{5}(7) } = \\ = \frac{9 log_{5}(7 \times 25) }{ log_{5}(7) } = \frac{9( log_{5}(7) + log_{5}(25) ) }{ log_{5}(7) } = \\ = \frac{9 log_{5}(7) + 9 log_{5}( {5}^{2} ) }{ log_{5}(7) } = \frac{9 log_{5}(7) + 9 \times 2 log_{5}(5) }{ log_{5}(7) } = \\ = \frac{9 log_{5}(7) + 18 }{ log_{5}(7) } = 9(1 + \frac{2}{ log_{5}(7) } )$

1) $\frac{log_{25}7}{log_{625}7}=\frac{log_{25}7}{log_{{25}^{2}}7}=\frac{log_{25}7}{\frac{1}{2}log_{25}7}=\frac{1}{1/2}=2$