What is 10log_{10}(56.27)-10log_{10}(33.52) ?

The solution to 10log_{10}(56.27)-10log_{10}(33.52) is log_{10}((5627^{10})/(2^{30)*419^{10}})

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simplify 10log_{10}(56.27)-10log_{10}(33.52)

simplify

10 lo g_{10} (56.27) - 10 lo g_{10} (33.52)

lo g_{10} (\frac{562 7 ^{10}}{2 ^{30} \cdot 41 9 ^{10}})

Decimal Notation

2.24972 \dots

Solution steps

10 lo g_{10} (56.27) - 10 lo g_{10} (33.52)

10 lo g_{10} (56.27) = 10 lo g_{10} (\frac{5627}{100})

lo g_{10} (33.52) = lo g_{10} (\frac{838}{25})

= 10 lo g_{10} (\frac{5627}{100}) - 10 lo g_{10} (\frac{838}{25})

10 lo g_{10} (\frac{5627}{100}) = lo g_{10} ((\frac{5627}{100})^{10})

- 10 lo g_{10} (\frac{838}{25}) = - lo g_{10} ((\frac{838}{25})^{10})

= lo g_{10} ((\frac{5627}{100})^{10}) - lo g_{10} ((\frac{838}{25})^{10})

Apply log rule:

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

lo g_{10} ((\frac{5627}{100})^{10}) - lo g_{10} ((\frac{838}{25})^{10}) = lo g_{10} (\frac{( \frac{5627}{100} ) ^{10}}{( \frac{838}{25} ) ^{10}})

= lo g_{10} (\frac{( \frac{5627}{100} ) ^{10}}{( \frac{838}{25} ) ^{10}})

\frac{( \frac{5627}{100} ) ^{10}}{( \frac{838}{25} ) ^{10}} = \frac{562 7 ^{10}}{2 ^{30} \cdot 41 9 ^{10}}

= lo g_{10} (\frac{562 7 ^{10}}{2 ^{30} \cdot 41 9 ^{10}})

ln (\frac{11}{0.5})

\frac{1}{16} ln (\frac{18}{10})

\frac{ln ( 18677 ) - ln ( 100 )}{ln ( 75000 ) - ln ( 100 )}

\frac{ln ( 2 ) - ln ( 1 0 ^{- 3} )}{ln ( 2 )}

\frac{- ln ( 2 )}{ln ( 364 ) - ln ( 365 )} + 1

What is 10log_{10}(56.27)-10log_{10}(33.52) ?
The solution to 10log_{10}(56.27)-10log_{10}(33.52) is log_{10}((5627^{10})/(2^{30)*419^{10}})