What is log_{10}(x/(4y)) ?

The solution to log_{10}(x/(4y)) is log_{10}(x)-2log_{10}(2)-log_{10}(y)

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simplify log_{10}(x/(4y))

simplify

lo g_{10} (\frac{x}{4 y})

lo g_{10} (x) - 2 lo g_{10} (2) - lo g_{10} (y)

Solution steps

lo g_{10} (\frac{x}{4 y})

Apply log rule:

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

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

= lo g_{10} (x) - lo g_{10} (4 y)

Simplify

lo g_{10} (4 y) : 2 lo g_{10} (2) + lo g_{10} (y)

= lo g_{10} (x) - (2 lo g_{10} (2) + lo g_{10} (y))

Apply the distributive law:

- (a + b) = - a - b

- (2 lo g_{10} (2) + lo g_{10} (y)) = - 2 lo g_{10} (2) - lo g_{10} (y)

= lo g_{10} (x) - 2 lo g_{10} (2) - lo g_{10} (y)

ln (\frac{1}{1 + 7})

\frac{1}{5} [lo g_{4} (x) + lo g_{4} (7)] - [lo g_{4} (y)]

(lo g_{a} (t) - lo g_{a} (s)) + 3 lo g_{a} (u)

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

What is log_{10}(x/(4y)) ?
The solution to log_{10}(x/(4y)) is log_{10}(x)-2log_{10}(2)-log_{10}(y)