What is 0.15*log_{10}(1.31)+0.65*log_{10}((45.57+176)/(60)) ?

The solution to 0.15*log_{10}(1.31)+0.65*log_{10}((45.57+176)/(60)) is log_{10}(2.43430…)

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simplify 0.15log_{10}(1.31)+0.65log_{10}((45.57+176)/(60))

simplify

0.15 \cdot lo g_{10} (1.31) + 0.65 \cdot lo g_{10} (\frac{45.57 + 176}{60})

lo g_{10} (2.43430 \dots)

Decimal Notation

0.38637 \dots

Solution steps

0.15 lo g_{10} (1.31) + 0.65 lo g_{10} (\frac{45.57 + 176}{60})

Apply log rule:

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

0.15 lo g_{10} (1.31) = lo g_{10} (1.3 1^{0.15})

= lo g_{10} (1.3 1^{0.15}) + 0.65 lo g_{10} (\frac{176 + 45.57}{60})

Apply log rule:

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

0.65 lo g_{10} (\frac{176 + 45.57}{60}) = lo g_{10} ((\frac{176 + 45.57}{60})^{0.65})

= lo g_{10} (1.3 1^{0.15}) + lo g_{10} ((\frac{176 + 45.57}{60})^{0.65})

Apply log rule:

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

lo g_{10} (1.3 1^{0.15}) + lo g_{10} ((\frac{45.57 + 176}{60})^{0.65}) = lo g_{10} (1.3 1^{0.15} (\frac{176 + 45.57}{60})^{0.65})

= lo g_{10} (1.3 1^{0.15} (\frac{176 + 45.57}{60})^{0.65})

1.3 1^{0.15} (\frac{45.57 + 176}{60})^{0.65} = 2.43430 \dots

= lo g_{10} (2.43430 \dots)

lo g_{e} (\frac{x}{e})

ln x^{2} + 4 - 2 ln (2)

\frac{1}{2} ln (\frac{y}{x})

lo g_{3} (\frac{x ^{2}}{y})

x - \frac{1}{2} lo g_{15} (17) + \frac{1}{2} lo g_{15} (3)

What is 0.15*log_{10}(1.31)+0.65*log_{10}((45.57+176)/(60)) ?
The solution to 0.15*log_{10}(1.31)+0.65*log_{10}((45.57+176)/(60)) is log_{10}(2.43430…)