What is log_{3}(x)-log_{3}(0.5) ?

The solution to log_{3}(x)-log_{3}(0.5) is log_{3}(2x)

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simplify log_{3}(x)-log_{3}(0.5)

simplify

lo g_{3} (x) - lo g_{3} (0.5)

lo g_{3} (2 x)

Solution steps

lo g_{3} (x) - lo g_{3} (0.5)

Apply log rule:

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

lo g_{3} (x) - lo g_{3} (0.5) = lo g_{3} (\frac{x}{0.5})

= lo g_{3} (\frac{x}{0.5})

Simplify

\frac{x}{0.5} : 2 x

= lo g_{3} (2 x)

ln (x - 6) - ln (x - 2) + 10 ln (x)

6 ln (\frac{1}{2})

ln (\frac{16}{15})

ln (64) + ln (7) - 5 ln (2)

- ln (75) - 3 ln (\frac{15}{22})

What is log_{3}(x)-log_{3}(0.5) ?
The solution to log_{3}(x)-log_{3}(0.5) is log_{3}(2x)