What is log_{a}(0.78)-log_{a}(6) ?

The solution to log_{a}(0.78)-log_{a}(6) is log_{a}(13/100)

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simplify log_{a}(0.78)-log_{a}(6)

simplify

lo g_{a} (0.78) - lo g_{a} (6)

lo g_{a} (\frac{13}{100})

Solution steps

lo g_{a} (0.78) - lo g_{a} (6)

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{a} (0.78) - lo g_{a} (6) = lo g_{a} (\frac{0.78}{6})

= lo g_{a} (\frac{0.78}{6})

\frac{0.78}{6} = \frac{13}{100}

= lo g_{a} (\frac{13}{100})

\frac{3}{4} lo g_{2} (x^{4}) - lo g_{2} (y)

- ln (\frac{2}{2}) + ln (1)

ln (\frac{x ^{4}}{( 3 x - 4 ) ^{2}})

\frac{1}{10} ln (\frac{10}{7})

lo g_{7} (\frac{y}{4})

What is log_{a}(0.78)-log_{a}(6) ?
The solution to log_{a}(0.78)-log_{a}(6) is log_{a}(13/100)