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

The solution to log_{10}(5)-2log_{10}(2) is log_{10}(5/4)

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

simplify

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

lo g_{10} (\frac{5}{4})

Decimal Notation

0.09691 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

2^{2} = 4

= lo g_{10} (\frac{5}{4})

lo g_{10} (\frac{p ^{5} + q}{100})

lo g_{e} (\frac{1}{10})

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

lo g_{10} (5 x^{5})

lo g_{c} (x^{4} y^{4} z)

What is log_{10}(5)-2log_{10}(2) ?
The solution to log_{10}(5)-2log_{10}(2) is log_{10}(5/4)