Question

XERCISE
If log,5 - a and log, 6 - b, then log,2 is equal
to​

Answer 1

Answer:

Property which is used constantly is

$log_{x}(y) = \frac{ log_{10}(y) }{ log_{10}(x) }$

Step-by-step explanation:

$log_{4}(5) = \frac{ log_{10}(5) }{ log_{10}(4) } = a$

$log_{5}(6) = \frac{ log_{10}(6) }{ log_{10}(5) } = b$

$\frac{ log_{10}(6) }{ log_{10}(4) } = a \times b$

$log_{10}(6) = log_{10}(3 \times 2) = log_{10}(3) + log_{10 }(2)$

also

$log_{10}(4) = 2 log_{10}(2)$

$a \times b = \frac{ log_{10}(3) + log_{10}(2) }{2 log_{10}(2) } \\ a \times b = \frac{1}{2} + \frac{ log_{2}(3) }{2}$

We know that

$log_{x}(y) = \frac{1}{ log_{y}(x) }$

$a \times b = \frac{1}{2} + \frac{1}{2 log_{3}(2) }$

$ab - \frac{1}{2} = \frac{1}{ 2log_{3}(2) } \\ \frac{2ab - 1}{2} = \frac{1}{2 log_{3}(2) } \\ 2log_{3}(2) = \frac{2}{2ab - 1} \\ log_{3}(2) = \frac{1}{2ab - 1}$