What is log_{10}(8)-2log_{10}(6)+log_{10}(3) ?

The solution to log_{10}(8)-2log_{10}(6)+log_{10}(3) is log_{10}(2/3)

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simplify log_{10}(8)-2log_{10}(6)+log_{10}(3)

simplify

lo g_{10} (8) - 2 lo g_{10} (6) + lo g_{10} (3)

lo g_{10} (\frac{2}{3})

Decimal Notation

- 0.17609 \dots

Solution steps

lo g_{10} (8) - 2 lo g_{10} (6) + lo g_{10} (3)

Apply log rule:

b \cdot lo g_{a} (x) = lo g_{a} (x^{b})

- 2 lo g_{10} (6) = - lo g_{10} (6^{2})

= lo g_{10} (8) - lo g_{10} (6^{2}) + lo g_{10} (3)

Apply log rule:

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

lo g_{10} (8) - lo g_{10} (6^{2}) = lo g_{10} (\frac{8}{6 ^{2}})

= lo g_{10} (\frac{8}{6 ^{2}}) + lo g_{10} (3)

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

lo g_{10} (\frac{8}{6 ^{2}}) + lo g_{10} (3) = lo g_{10} (\frac{8}{6 ^{2}} \cdot 3)

= lo g_{10} (\frac{8}{6 ^{2}} \cdot 3)

\frac{8}{6 ^{2}} \cdot 3 = \frac{2}{3}

= lo g_{10} (\frac{2}{3})

lo g_{a} (6 x y^{5} z^{4})

5 lo g_{10} (3) + lo g_{10} (4)

lo g_{10} (k^{2} - 100) - lo g_{10} (k) - 10

ln (\frac{3 d}{4 ^{- 1}})

What is log_{10}(8)-2log_{10}(6)+log_{10}(3) ?
The solution to log_{10}(8)-2log_{10}(6)+log_{10}(3) is log_{10}(2/3)