What is 10log_{10}(1/86400 (10^{115/10})) ?

The solution to 10log_{10}(1/86400 (10^{115/10})) is -10log_{10}(86400)+115

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simplify 10log_{10}(1/86400 (10^{115/10}))

simplify

10 lo g_{10} (\frac{1}{86400} (1 0^{\frac{115}{10}}))

- 10 lo g_{10} (86400) + 115

Decimal Notation

65.63486 \dots

Solution steps

10 lo g_{10} (\frac{1}{86400} (1 0^{\frac{115}{10}}))

Apply log rule:

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

10 lo g_{10} (\frac{1}{86400} (1 0^{\frac{115}{10}})) = 10 lo g_{10} (\frac{1}{86400}) + 10 lo g_{10} (1 0^{\frac{115}{10}})

= 10 lo g_{10} (\frac{1}{86400}) + 10 lo g_{10} (1 0^{\frac{115}{10}})

Apply log rule:

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

lo g_{10} (1 0^{\frac{115}{10}}) = \frac{115}{10} lo g_{10} (10)

= 10 lo g_{10} (\frac{1}{86400}) + 10 \cdot \frac{115}{10} lo g_{10} (10)

Apply log rule:

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

lo g_{10} (\frac{1}{86400}) = lo g_{10} (1) - lo g_{10} (86400)

= 10 (lo g_{10} (1) - lo g_{10} (86400)) + 10 \cdot \frac{115}{10} lo g_{10} (10)

10 (lo g_{10} (1) - lo g_{10} (86400)) = - 10 lo g_{10} (86400)

= - 10 lo g_{10} (86400) + 10 \cdot \frac{115}{10} lo g_{10} (10)

10 \cdot \frac{115}{10} lo g_{10} (10) = 115

= - 10 lo g_{10} (86400) + 115

ln (\frac{19.738}{1.9738})

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

ln (\frac{- x}{x ^{2} - 3})

- lo g_{10} (9 \cdot 1 0^{- 9})

\frac{7}{2} ln ∣ 2 (0.5 - 3) ∣ - \frac{7}{2} ln ∣ 2 (- 0.5 - 3) ∣

What is 10log_{10}(1/86400 (10^{115/10})) ?
The solution to 10log_{10}(1/86400 (10^{115/10})) is -10log_{10}(86400)+115