What is log_{3}(7)+1/2 log_{3}(t)-log_{3}(r) ?

The solution to log_{3}(7)+1/2 log_{3}(t)-log_{3}(r) is log_{3}(7/r)+(log_{3}(t))/2

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simplify log_{3}(7)+1/2 log_{3}(t)-log_{3}(r)

simplify

lo g_{3} (7) + \frac{1}{2} lo g_{3} (t) - lo g_{3} (r)

lo g_{3} (\frac{7}{r}) + \frac{lo g _{3} ( t )}{2}

Solution steps

lo g_{3} (7) + \frac{1}{2} lo g_{3} (t) - lo g_{3} (r)

Apply log rule:

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

lo g_{3} (7) - lo g_{3} (r) = lo g_{3} (\frac{7}{r})

= lo g_{3} (\frac{7}{r}) + \frac{1}{2} lo g_{3} (t)

Simplify

\frac{1}{2} lo g_{3} (t) : \frac{lo g _{3} ( t )}{2}

= lo g_{3} (\frac{7}{r}) + \frac{lo g _{3} ( t )}{2}

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

lo g_{10} (\frac{100 x ^{2}}{27})

lo g_{10} (\frac{y}{10000})

2 lo g_{10} (2) + lo g_{10} (3)

ln (\frac{y}{2 ^{y}} \cdot (2 - x)^{y - 1})

What is log_{3}(7)+1/2 log_{3}(t)-log_{3}(r) ?
The solution to log_{3}(7)+1/2 log_{3}(t)-log_{3}(r) is log_{3}(7/r)+(log_{3}(t))/2