Question

Acest ex .Vă mulțumesc !​

Answer 1

Răspuns:

Explicație pas cu pas:

Answer 2

Explicație pas cu pas:

$a = log_{176}(484) = \frac{ ln( {2}^{2} \cdot {11}^{2} ) }{ ln( {2}^{4} \cdot 11) } = \frac{2 ln(2) + 2 ln(11)}{4 ln(2) + ln(11)} = \frac{2 \frac{ln(2) }{ ln(11) } + 2}{4\frac{ln(2) }{ ln(11) } + 1} = \frac{2 log_{11}(2) + 2}{4log_{11}(2) + 1}$

$log_{11}(2) = t \implies$

$a = \frac{2t + 2}{4t + 1} \iff 4ta + a = 2t + 2 \\ 2t(2a - 1) = 2 - a \iff t = \frac{2 - a}{2(2a - 1)}$

$log_{44}(242) = \frac{ ln(2 \cdot {11}^{2} ) }{ ln( {2}^{2} \cdot 11) } = \frac{ln(2) + 2 ln(11)}{2 ln(2) + ln(11)} = \\ = \frac{\frac{ln(2) }{ ln(11) } + 2}{2\frac{ln(2) }{ ln(11) } + 1} = \frac{t + 2}{2t + 1} = \frac{\frac{2 - a}{2(2a - 1)} + 2}{\frac{2(2 - a)}{2(2a - 1)} + 1} \\ = \frac{2 - a + 4(2a - 1)}{2(2 - a) + 2(2a - 1)} = \frac{2 - a + 8a - 4}{4 - 2a + 4a - 2} \\ = \frac{7a - 2}{2a + 2} = \bf \frac{7a - 2}{2(a + 1)}$