Question

Выразите искомый логарифм через заданный:
1) Найти log6(9), если log6(2)=a
2) Найти log98(28), если log2(7)=a

Answer 1

1)

$log6_{2}  = a => 2^a = 6\\log6_{9} = log2^a_{9} = a * log2_{9}$

2)

$log2_{7}  = a => 7^a = 2\\log98_{28} = 1  / log28_{98} = 1  / log(7 * 2 * 2)_{98} =\\\\ 1  /( log7_{98} + log2_{98} + log2_{98}) = 1  /( log7_{98} + log7^a_{98} + log7^a_{98}) = 1  /log(7 * 7^{2a} )_{98} = \\\\ 1  /log(7^{2a + 1} )_{98} = 1 / ((2a + 1) * log7_{98}) = log98_{7} / (2a + 1) =\\\\ log(7^2 * 2)_{7} / (2a + 1) = (2 + log2_{7}) / (2a + 1) = \frac{2 + a}{2a + 1}$