What is log_{10}(2)-2log_{10}(5) ?

The solution to log_{10}(2)-2log_{10}(5) is log_{10}(2/25)

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simplify log_{10}(2)-2log_{10}(5)

simplify

lo g_{10} (2) - 2 lo g_{10} (5)

lo g_{10} (\frac{2}{25})

Decimal Notation

- 1.09691 \dots

Solution steps

lo g_{10} (2) - 2 lo g_{10} (5)

Apply log rule:

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

- 2 lo g_{10} (5) = - lo g_{10} (5^{2})

= lo g_{10} (2) - lo g_{10} (5^{2})

Apply log rule:

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

lo g_{10} (2) - lo g_{10} (5^{2}) = lo g_{10} (\frac{2}{5 ^{2}})

= lo g_{10} (\frac{2}{5 ^{2}})

5^{2} = 25

= lo g_{10} (\frac{2}{25})

lo g_{7} (5 y (3 y + 4))

lo g_{4} (x^{2} - 9) - 5 lo g_{4} (x + 3)

ln (\frac{7}{8})

lo g_{b} (y^{2} z)

lo g_{10} (2) + lo g_{10} (x)

What is log_{10}(2)-2log_{10}(5) ?
The solution to log_{10}(2)-2log_{10}(5) is log_{10}(2/25)