What is log_{3}(10)-log_{3}(5)log_{3}(18) ?

The solution to log_{3}(10)-log_{3}(5)log_{3}(18) is log_{3}(1/(5*2^{log_{3)(5)-1}})

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simplify log_{3}(10)-log_{3}(5)log_{3}(18)

simplify

lo g_{3} (10) - lo g_{3} (5) lo g_{3} (18)

lo g_{3} (\frac{1}{5 \cdot 2 ^{l o g_{3} (5) - 1}})

Decimal Notation

- 1.75833 \dots

Solution steps

lo g_{3} (10) - lo g_{3} (5) lo g_{3} (18)

Apply log rule:

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

lo g_{3} (5) lo g_{3} (18) = lo g_{3} (1 8^{l o g_{3} (5)})

= lo g_{3} (10) - lo g_{3} (1 8^{l o g_{3} (5)})

Apply log rule:

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

lo g_{3} (10) - lo g_{3} (1 8^{l o g_{3} (5)}) = lo g_{3} (\frac{10}{1 8 ^{l o g_{3} (5)}})

= lo g_{3} (\frac{10}{1 8 ^{l o g_{3} (5)}})

\frac{10}{1 8 ^{l o g_{3} (5)}} = \frac{1}{5 \cdot 2 ^{l o g_{3} (5) - 1}}

= lo g_{3} (\frac{1}{5 \cdot 2 ^{l o g_{3} (5) - 1}})

lo g_{b} (2) + 2 lo g_{b} (x)

ln (3) (- 1 - \frac{1}{2} - \frac{1}{8} + \frac{3}{4}) + ln (2) (1 - \frac{1}{4} - \frac{3}{4})

ln (1) - ln (\frac{3}{2})

lo g_{10} (5 x) - lo g_{10} (4 y)

lo g_{b} (\frac{x ^{2}}{y ^{3} z ^{4}})

What is log_{3}(10)-log_{3}(5)log_{3}(18) ?
The solution to log_{3}(10)-log_{3}(5)log_{3}(18) is log_{3}(1/(5*2^{log_{3)(5)-1}})