What is log_{10}(6)-log_{10}(3)+2log_{10}(7) ?

The solution to log_{10}(6)-log_{10}(3)+2log_{10}(7) is log_{10}(98)

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simplify log_{10}(6)-log_{10}(3)+2log_{10}(7)

simplify

lo g_{10} (6) - lo g_{10} (3) + 2 lo g_{10} (7)

lo g_{10} (98)

Decimal Notation

1.99122 \dots

Solution steps

lo g_{10} (6) - lo g_{10} (3) + 2 lo g_{10} (7)

Apply log rule:

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

2 lo g_{10} (7) = lo g_{10} (7^{2})

= lo g_{10} (6) - lo g_{10} (3) + lo g_{10} (7^{2})

Apply log rule:

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

lo g_{10} (6) - lo g_{10} (3) = lo g_{10} (\frac{6}{3})

= lo g_{10} (\frac{6}{3}) + lo g_{10} (7^{2})

Apply log rule:

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

lo g_{10} (\frac{6}{3}) + lo g_{10} (7^{2}) = lo g_{10} (\frac{6}{3} \cdot 7^{2})

= lo g_{10} (\frac{6}{3} \cdot 7^{2})

\frac{6}{3} \cdot 7^{2} = 98

= lo g_{10} (98)

lo g_{3} (\frac{9}{x - 1})

ln (\frac{e}{x})

lo g_{4} (5 x^{2})

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

ln (\frac{7}{4})

What is log_{10}(6)-log_{10}(3)+2log_{10}(7) ?
The solution to log_{10}(6)-log_{10}(3)+2log_{10}(7) is log_{10}(98)