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} \cdot 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} \cdot 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

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