What is log_{10}(10)+2log_{10}(3)+log_{10}(7) ?

The solution to log_{10}(10)+2log_{10}(3)+log_{10}(7) is log_{10}(630)

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simplify log_{10}(10)+2log_{10}(3)+log_{10}(7)

simplify

lo g_{10} (10) + 2 lo g_{10} (3) + lo g_{10} (7)

lo g_{10} (630)

Decimal Notation

2.79934 \dots

Solution steps

lo g_{10} (10) + 2 lo g_{10} (3) + lo g_{10} (7)

Apply log rule:

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

2 lo g_{10} (3) = lo g_{10} (3^{2})

= lo g_{10} (10) + lo g_{10} (3^{2}) + lo g_{10} (7)

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

lo g_{10} (10) + lo g_{10} (3^{2}) = lo g_{10} (10 \cdot 3^{2})

= lo g_{10} (10 \cdot 3^{2}) + lo g_{10} (7)

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

lo g_{10} (10 \cdot 3^{2}) + lo g_{10} (7) = lo g_{10} (10 \cdot 3^{2} \cdot 7)

= lo g_{10} (10 \cdot 3^{2} \cdot 7)

10 \cdot 3^{2} \cdot 7 = 630

= lo g_{10} (630)

ln (sin (3) x^{5})

2 ln (x) - 4 ln (x^{2} + 1) + 2 ln (x - 1)

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

ln (x^{10} 5 - x)

lo g_{7} (8 yz)

What is log_{10}(10)+2log_{10}(3)+log_{10}(7) ?
The solution to log_{10}(10)+2log_{10}(3)+log_{10}(7) is log_{10}(630)