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

The solution to log_{8}(10)-2log_{8}(3) is log_{8}(10/9)

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

simplify

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

lo g_{8} (\frac{10}{9})

Decimal Notation

0.05066 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

3^{2} = 9

= lo g_{8} (\frac{10}{9})

lo g_{10} (MN)

lo g_{2} (3 x y^{2})

lo g_{\frac{3}{5}} (\frac{4}{9}) \cdot lo g_{\frac{3}{2}} (\frac{25}{9})

lo g_{10} (\frac{9 b}{10})

3 ln (3) - 3 ln (2)

What is log_{8}(10)-2log_{8}(3) ?
The solution to log_{8}(10)-2log_{8}(3) is log_{8}(10/9)