What is log_{10}(4/(ab)) ?

The solution to log_{10}(4/(ab)) is 2log_{10}(2)-log_{10}(a)-log_{10}(b)

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simplify log_{10}(4/(ab))

simplify

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

2 lo g_{10} (2) - lo g_{10} (a) - lo g_{10} (b)

Solution steps

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

Apply log rule:

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

lo g_{10} (\frac{4}{ab}) = lo g_{10} (4) - lo g_{10} (ab)

= lo g_{10} (4) - lo g_{10} (ab)

lo g_{10} (4) = 2 lo g_{10} (2)

lo g_{10} (ab) = lo g_{10} (a) + lo g_{10} (b)

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

Apply the distributive law:

- (a + b) = - a - b

- (lo g_{10} (a) + lo g_{10} (b)) = - lo g_{10} (a) - lo g_{10} (b)

= 2 lo g_{10} (2) - lo g_{10} (a) - lo g_{10} (b)

ln ((sin (x))^{l n (x)})

ln (\frac{2000}{10})

lo g_{10} (\frac{x ( x + 4 )}{( x + 7 ) ^{7}})

ln (n + 1) - ln (n)

lo g_{2} (5) + \frac{1}{4} lo g_{2} (x)

What is log_{10}(4/(ab)) ?
The solution to log_{10}(4/(ab)) is 2log_{10}(2)-log_{10}(a)-log_{10}(b)