What is log_{10}(x/(yz)) ?

The solution to log_{10}(x/(yz)) is log_{10}(x)-log_{10}(y)-log_{10}(z)

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simplify log_{10}(x/(yz))

simplify

lo g_{10} (\frac{x}{yz})

lo g_{10} (x) - lo g_{10} (y) - lo g_{10} (z)

Solution steps

lo g_{10} (\frac{x}{yz})

Apply log rule:

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

lo g_{10} (\frac{x}{yz}) = lo g_{10} (x) - lo g_{10} (yz)

= lo g_{10} (x) - lo g_{10} (yz)

Simplify

lo g_{10} (yz) : lo g_{10} (y) + lo g_{10} (z)

= lo g_{10} (x) - (lo g_{10} (y) + lo g_{10} (z))

Apply the distributive law:

- (a + b) = - a - b

- (lo g_{10} (y) + lo g_{10} (z)) = - lo g_{10} (y) - lo g_{10} (z)

= lo g_{10} (x) - lo g_{10} (y) - lo g_{10} (z)

ln (csc (x)) - ln (cot (x))

ln (\frac{3}{8})

ln (4) + ln (x)

lo g_{6} (\frac{64 x ^{3} ( 4 x + 1 )}{2 x - 1})

lo g_{10} (b) + 2 lo g_{10} (c)

What is log_{10}(x/(yz)) ?
The solution to log_{10}(x/(yz)) is log_{10}(x)-log_{10}(y)-log_{10}(z)