What is log_{2}(6)-log_{2}(15)log_{2}(20) ?

The solution to log_{2}(6)-log_{2}(15)log_{2}(20) is log_{2}(2/(75*5^{log_{2)(15)}})

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simplify log_{2}(6)-log_{2}(15)log_{2}(20)

simplify

lo g_{2} (6) - lo g_{2} (15) lo g_{2} (20)

lo g_{2} (\frac{2}{75 \cdot 5 ^{l o g_{2} (15)}})

Decimal Notation

- 14.30033 \dots

Solution steps

lo g_{2} (6) - lo g_{2} (15) lo g_{2} (20)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

lo g_{2} (15) lo g_{2} (20) = lo g_{2} (2 0^{l o g_{2} (15)})

= lo g_{2} (6) - lo g_{2} (2 0^{l o g_{2} (15)})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

lo g_{2} (6) - lo g_{2} (2 0^{l o g_{2} (15)}) = lo g_{2} (\frac{6}{2 0 ^{l o g_{2} (15)}})

= lo g_{2} (\frac{6}{2 0 ^{l o g_{2} (15)}})

\frac{6}{2 0 ^{l o g_{2} (15)}} = \frac{2}{75 \cdot 5 ^{l o g_{2} (15)}}

= lo g_{2} (\frac{2}{75 \cdot 5 ^{l o g_{2} (15)}})

2 ln (x^{0.5} y^{0.5})

- \frac{2}{3} lo g_{10} (x) - 2 lo g_{10} (y)

1 + \frac{1}{2} lo g_{10} (p + 4) - lo g_{10} (x)

7 ln (x + 9) - 8 ln (x)

ln (\frac{y}{x} - 4) + 6 (\frac{1}{5} ln (\frac{y}{x} - 1) - \frac{1}{5} ln (\frac{y}{x} + 4)) + ln (x)

What is log_{2}(6)-log_{2}(15)log_{2}(20) ?
The solution to log_{2}(6)-log_{2}(15)log_{2}(20) is log_{2}(2/(75*5^{log_{2)(15)}})