What is log_{10}(7)+2log_{10}(3)-log_{10}(4) ?

The solution to log_{10}(7)+2log_{10}(3)-log_{10}(4) is log_{10}(63/4)

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simplify log_{10}(7)+2log_{10}(3)-log_{10}(4)

simplify

lo g_{10} (7) + 2 lo g_{10} (3) - lo g_{10} (4)

lo g_{10} (\frac{63}{4})

Decimal Notation

1.19728 \dots

Solution steps

lo g_{10} (7) + 2 lo g_{10} (3) - lo g_{10} (4)

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} (7) + lo g_{10} (3^{2}) - lo g_{10} (4)

Apply log rule:

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

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

= lo g_{10} (7 \cdot 3^{2}) - lo g_{10} (4)

Apply log rule:

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

lo g_{10} (7 \cdot 3^{2}) - lo g_{10} (4) = lo g_{10} (\frac{7 \cdot 3 ^{2}}{4})

= lo g_{10} (\frac{7 \cdot 3 ^{2}}{4})

7 \cdot 3^{2} = 63

= lo g_{10} (\frac{63}{4})

6 ln (x) - \frac{1}{5} ln (y)

3^{\frac{l n ( \frac{4}{l n ( 3 )} )}{l n ( 3 )}} ln (3)

lo g_{8} (7 x)

2 lo g_{10} (a) + 4 lo g_{10} (b^{2}) - lo g_{10} (a) b

ln (2.5 \cdot 1 0^{- 3}) + (\frac{130000}{8.314 \cdot 473})

What is log_{10}(7)+2log_{10}(3)-log_{10}(4) ?
The solution to log_{10}(7)+2log_{10}(3)-log_{10}(4) is log_{10}(63/4)