What is simplify-log_{10}((0.00174*660+10*2.35)/(670)) ?

The solution to simplify-log_{10}((0.00174*660+10*2.35)/(670)) is -log_{10}(24.6484)+log_{10}(670)

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simplify-log_{10}((0.00174660+102.35)/(670))

simplify

- lo g_{10} (\frac{0.00174 \cdot 660 + 10 \cdot 2.35}{670})

- lo g_{10} (24.6484) + lo g_{10} (670)

Decimal Notation

1.43428 \dots

Solution steps

- lo g_{10} (\frac{0.00174 \cdot 660 + 10 \cdot 2.35}{670})

Apply log rule:

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

lo g_{10} (\frac{0.00174 \cdot 660 + 10 \cdot 2.35}{670}) = lo g_{10} (0.00174 \cdot 660 + 10 \cdot 2.35) - lo g_{10} (670)

= - (lo g_{10} (660 \cdot 0.00174 + 10 \cdot 2.35) - lo g_{10} (670))

lo g_{10} (0.00174 \cdot 660 + 10 \cdot 2.35) = lo g_{10} (24.6484)

= - (lo g_{10} (24.6484) - lo g_{10} (670))

Distribute parentheses

= - (lo g_{10} (24.6484)) - (- lo g_{10} (670))

Apply minus-plus rules

- (- a) = a, - (a) = - a

= - lo g_{10} (24.6484) + lo g_{10} (670)

(lo g_{c} (x) - lo g_{c} (y)) + 2 lo g_{c} (v)

ln (\frac{1}{2.7})

2 ln (\frac{401}{2})

\frac{6}{7} lo g_{2} (\frac{6}{7}) + \frac{1}{7} lo g_{2} (\frac{1}{7})

3 ln (\frac{7}{2}) + 10

What is simplify-log_{10}((0.00174*660+10*2.35)/(670)) ?
The solution to simplify-log_{10}((0.00174*660+10*2.35)/(670)) is -log_{10}(24.6484)+log_{10}(670)