What is log_{3}(2z)-log_{3}(x) ?

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

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simplify log_{3}(2z)-log_{3}(x)

simplify

lo g_{3} (2 z) - lo g_{3} (x)

lo g_{3} (\frac{2 z}{x})

Solution steps

lo g_{3} (2 z) - lo g_{3} (x)

Apply log rule:

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

lo g_{3} (2 z) - lo g_{3} (x) = lo g_{3} (\frac{2 z}{x})

= lo g_{3} (\frac{2 z}{x})

\frac{8}{12} lo g_{2} (\frac{8}{12}) + \frac{4}{12} lo g_{2} (\frac{4}{12})

lo g_{10} ((19 y)^{6})

lo g_{3} (27 (x^{2} - 49))

lo g_{2} (9) - lo g_{2} (y) + \frac{1}{2} lo g_{2} (x)

\frac{1}{18} ln (\frac{167}{23})

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