What is log_{10}(14)+1/2 log_{10}(3)-log_{10}(2) ?

The solution to log_{10}(14)+1/2 log_{10}(3)-log_{10}(2) is log_{10}(7sqrt(3))

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simplify log_{10}(14)+1/2 log_{10}(3)-log_{10}(2)

simplify

lo g_{10} (14) + \frac{1}{2} lo g_{10} (3) - lo g_{10} (2)

lo g_{10} (73)

Decimal Notation

1.08365 \dots

Solution steps

lo g_{10} (14) + \frac{1}{2} lo g_{10} (3) - lo g_{10} (2)

Apply log rule:

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

\frac{1}{2} lo g_{10} (3) = lo g_{10} (3^{\frac{1}{2}})

= lo g_{10} (14) + lo g_{10} (3^{\frac{1}{2}}) - lo g_{10} (2)

Apply log rule:

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

lo g_{10} (14) + lo g_{10} (3^{\frac{1}{2}}) = lo g_{10} (14 \cdot 3^{\frac{1}{2}})

= lo g_{10} (14 \cdot 3^{\frac{1}{2}}) - lo g_{10} (2)

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{10} (14 \cdot 3^{\frac{1}{2}}) - lo g_{10} (2) = lo g_{10} (\frac{14 \cdot 3 ^{\frac{1}{2}}}{2})

= lo g_{10} (\frac{14 \cdot 3 ^{\frac{1}{2}}}{2})

Divide the numbers:

\frac{14}{2} = 7

= lo g_{10} (7 \cdot 3^{\frac{1}{2}})

Apply exponent rule:

a^{\frac{1}{2}} = a

3^{\frac{1}{2}} = 3

= lo g_{10} (73)

lo g_{5} (a^{2} + 10 a + 9) - lo g_{5} (a + 9) + 2

lo g_{10} (7.2) - lo g_{10} (6.7)

ln (12) - ln (5)

2 ln (5 y) + \frac{1}{x}

- \frac{3}{9} lo g_{2} (\frac{3}{9}) - \frac{6}{9} lo g_{2} (\frac{6}{9})

What is log_{10}(14)+1/2 log_{10}(3)-log_{10}(2) ?
The solution to log_{10}(14)+1/2 log_{10}(3)-log_{10}(2) is log_{10}(7sqrt(3))