What is log_{10}((8c)/(10)) ?

The solution to log_{10}((8c)/(10)) is 2log_{10}(2)+log_{10}(c)-log_{10}(5)

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simplify log_{10}((8c)/(10))

simplify

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

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

Solution steps

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

Cancel

\frac{8 c}{10} : \frac{4 c}{5}

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

Apply log rule:

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

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

= lo g_{10} (4 c) - lo g_{10} (5)

Simplify

lo g_{10} (4 c) : 2 lo g_{10} (2) + lo g_{10} (c)

= 2 lo g_{10} (2) + lo g_{10} (c) - lo g_{10} (5)

lo g_{10} (0.5) + lo g_{10} (\frac{1}{2})

lo g_{9} (\frac{11}{17}) + lo g_{9} (\frac{17}{11})

ln (\frac{17}{7})

lo g_{b} (x yz)

6 ln (4) - 2 ln (7) + 6 ln (12) - 2 ln (5)

What is log_{10}((8c)/(10)) ?
The solution to log_{10}((8c)/(10)) is 2log_{10}(2)+log_{10}(c)-log_{10}(5)