What is 20log_{10}(0.25)+20log_{10}(5.8)+92.45 ?

The solution to 20log_{10}(0.25)+20log_{10}(5.8)+92.45 is log_{10}(1687.95181…)+92.45

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simplify 20log_{10}(0.25)+20log_{10}(5.8)+92.45

simplify

20 lo g_{10} (0.25) + 20 lo g_{10} (5.8) + 92.45

lo g_{10} (1687.95181 \dots) + 92.45

Decimal Notation

95.67736 \dots

Solution steps

20 lo g_{10} (0.25) + 20 lo g_{10} (5.8) + 92.45

Apply log rule:

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

20 lo g_{10} (0.25) = lo g_{10} (0.2 5^{20})

= lo g_{10} (0.2 5^{20}) + 20 lo g_{10} (5.8) + 92.45

Apply log rule:

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

20 lo g_{10} (5.8) = lo g_{10} (5. 8^{20})

= lo g_{10} (0.2 5^{20}) + lo g_{10} (5. 8^{20}) + 92.45

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

lo g_{10} (0.2 5^{20}) + lo g_{10} (5. 8^{20}) = lo g_{10} (0.2 5^{20} \cdot 5. 8^{20})

= lo g_{10} (0.2 5^{20} \cdot 5. 8^{20}) + 92.45

0.2 5^{20} \cdot 5. 8^{20} = 1687.95181 \dots

= lo g_{10} (1687.95181 \dots) + 92.45

ln (\frac{x ^{x}}{x ^{2} - 1})

ln (\frac{1.2}{1.06})

- lo g_{10} (1.73 (1 0^{- 5}))

ln (10 x)

\frac{1}{6} (ln (3) - ln (5))

What is 20log_{10}(0.25)+20log_{10}(5.8)+92.45 ?
The solution to 20log_{10}(0.25)+20log_{10}(5.8)+92.45 is log_{10}(1687.95181…)+92.45