What is log_{10}(3)+log_{10}(6)-2log_{10}(4) ?

The solution to log_{10}(3)+log_{10}(6)-2log_{10}(4) is log_{10}(9/8)

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simplify log_{10}(3)+log_{10}(6)-2log_{10}(4)

simplify

lo g_{10} (3) + lo g_{10} (6) - 2 lo g_{10} (4)

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

Decimal

0.05115 \dots

Solution steps

lo g_{10} (3) + lo g_{10} (6) - 2 lo g_{10} (4)

Apply log rule:

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

- 2 lo g_{10} (4) = - lo g_{10} (4^{2})

= lo g_{10} (3) + lo g_{10} (6) - lo g_{10} (4^{2})

Apply log rule:

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

lo g_{10} (3) + lo g_{10} (6) = lo g_{10} (3 \cdot 6)

= lo g_{10} (3 \cdot 6) - lo g_{10} (4^{2})

Apply log rule:

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

lo g_{10} (3 \cdot 6) - lo g_{10} (4^{2}) = lo g_{10} (\frac{3 \cdot 6}{4 ^{2}})

= lo g_{10} (\frac{3 \cdot 6}{4 ^{2}})

Cancel

\frac{3 \cdot 6}{4 ^{2}} : \frac{9}{8}

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

\frac{1}{4} ln (2)

3 ln (x) + 5 ln (y) - 4 ln (z)

ln (14 x y)

\frac{lo g _{10} ( 4 )}{lo g _{10} ( 5 ) - lo g _{10} ( 4 )}

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

What is log_{10}(3)+log_{10}(6)-2log_{10}(4) ?
The solution to log_{10}(3)+log_{10}(6)-2log_{10}(4) is log_{10}(9/8)