What is 1/2 log_{10}(17)-log_{10}(5) ?

The solution to 1/2 log_{10}(17)-log_{10}(5) is log_{10}((17^{1/2})/5)

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simplify 1/2 log_{10}(17)-log_{10}(5)

simplify

\frac{1}{2} lo g_{10} (17) - lo g_{10} (5)

lo g_{10} (\frac{1 7 ^{\frac{1}{2}}}{5})

Decimal Notation

- 0.08374 \dots

Solution steps

\frac{1}{2} lo g_{10} (17) - lo g_{10} (5)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{1}{2} lo g_{10} (17) = lo g_{10} (1 7^{\frac{1}{2}})

= lo g_{10} (1 7^{\frac{1}{2}}) - lo g_{10} (5)

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

lo g_{10} (1 7^{\frac{1}{2}}) - lo g_{10} (5) = lo g_{10} (\frac{1 7 ^{\frac{1}{2}}}{5})

= lo g_{10} (\frac{1 7 ^{\frac{1}{2}}}{5})

ln (\frac{n - 2}{n})

lo g_{10} (x) + \frac{1}{2} lo g_{10} (y) - 2 lo g_{10} (z)

ln (x e^{- 0.06 x})

lo g_{e} (\frac{x ^{2} + 6 x - 1}{x + 1})

lo g_{7} ((\frac{x ^{6}}{y})^{4})

What is 1/2 log_{10}(17)-log_{10}(5) ?
The solution to 1/2 log_{10}(17)-log_{10}(5) is log_{10}((17^{1/2})/5)