What is 1/2 log_{3}(((27b^2))/c) ?

The solution to 1/2 log_{3}(((27b^2))/c) is (3-log_{3}(c))/2+log_{3}(b)

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simplify 1/2 log_{3}(((27b^2))/c)

simplify

\frac{1}{2} lo g_{3} (\frac{( 27 b ^{2} )}{c})

\frac{3 - lo g _{3} ( c )}{2} + lo g_{3} (b)

Solution steps

\frac{1}{2} lo g_{3} (\frac{27 b ^{2}}{c})

Simplify

lo g_{3} (\frac{27 b ^{2}}{c}) : 3 + 2 lo g_{3} (b) - lo g_{3} (c)

= \frac{1}{2} (3 + 2 lo g_{3} (b) - lo g_{3} (c))

Expand

\frac{1}{2} (3 + 2 lo g_{3} (b) - lo g_{3} (c)) : \frac{3 - lo g _{3} ( c )}{2} + lo g_{3} (b)

= \frac{3 - lo g _{3} ( c )}{2} + lo g_{3} (b)

ln (18.2) - ln (3)

lo g_{10} (\frac{a ^{3}}{b ^{2} \cdot 2})

\frac{3}{5} lo g_{2} (\frac{3}{5}) + \frac{2}{5} lo g_{2} (\frac{2}{5})

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

16.7 + 10 \cdot lo g_{10} (\frac{750}{100})

What is 1/2 log_{3}(((27b^2))/c) ?
The solution to 1/2 log_{3}(((27b^2))/c) is (3-log_{3}(c))/2+log_{3}(b)