What is 3*log_{2}(3)-2log_{2}(5) ?

The solution to 3*log_{2}(3)-2log_{2}(5) is log_{2}(27/25)

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simplify 3*log_{2}(3)-2log_{2}(5)

simplify

3 \cdot lo g_{2} (3) - 2 lo g_{2} (5)

lo g_{2} (\frac{27}{25})

Decimal Notation

0.11103 \dots

Solution steps

3 lo g_{2} (3) - 2 lo g_{2} (5)

3 lo g_{2} (3) = lo g_{2} (3^{3})

- 2 lo g_{2} (5) = - lo g_{2} (5^{2})

= lo g_{2} (3^{3}) - lo g_{2} (5^{2})

Apply log rule:

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

lo g_{2} (3^{3}) - lo g_{2} (5^{2}) = lo g_{2} (\frac{3 ^{3}}{5 ^{2}})

= lo g_{2} (\frac{3 ^{3}}{5 ^{2}})

\frac{3 ^{3}}{5 ^{2}} = \frac{27}{25}

= lo g_{2} (\frac{27}{25})

lo g_{3} (x + 2) + lo g_{3} (5)

ln (9 x^{2})

ln (\frac{e ^{- (x - θ)}}{( 1 + e ^{- (x - θ)} ) ^{2}})

ln (\frac{e ^{\frac{9}{2}} 2 ( x )}{x ^{3}}) - ln ((y - 2)^{3} h (x))

\frac{1}{2} (lo g_{8} (s) + lo g_{8} (t))

What is 3*log_{2}(3)-2log_{2}(5) ?
The solution to 3*log_{2}(3)-2log_{2}(5) is log_{2}(27/25)