What is log_{a}(bc)+log_{b}(ca) ?

The solution to log_{a}(bc)+log_{b}(ca) is log_{a}(b)+log_{a}(c)+log_{b}(c)+log_{b}(a)

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simplify log_{a}(bc)+log_{b}(ca)

simplify

lo g_{a} (b c) + lo g_{b} (c a)

lo g_{a} (b) + lo g_{a} (c) + lo g_{b} (c) + lo g_{b} (a)

Solution steps

lo g_{a} (b c) + lo g_{b} (c a)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

lo g_{a} (b c) = lo g_{a} (b) + lo g_{a} (c), lo g_{b} (c a) = lo g_{b} (c) + lo g_{b} (a)

= lo g_{a} (b) + lo g_{a} (c) + lo g_{b} (c) + lo g_{b} (a)

ln (\frac{75}{49})

ln (ln (\frac{1}{1 - 0.02})) - ln (ln (\frac{1}{1 - 0.003}))

2.45 + lo g_{10} (\frac{0.022}{0.069})

(0.287) ln (\frac{500}{200})

2 lo g_{3} (2) - 3 lo g_{3} (4) - 2 lo g_{3} (5)

What is log_{a}(bc)+log_{b}(ca) ?
The solution to log_{a}(bc)+log_{b}(ca) is log_{a}(b)+log_{a}(c)+log_{b}(c)+log_{b}(a)