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

The solution to log_{4}((ab)/(cd)) is log_{4}(a)+log_{4}(b)-log_{4}(c)-log_{4}(d)

Popular >

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

simplify

lo g_{4} (\frac{ab}{c d})

lo g_{4} (a) + lo g_{4} (b) - lo g_{4} (c) - lo g_{4} (d)

Solution steps

lo g_{4} (\frac{ab}{c d})

Apply log rule:

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

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

= lo g_{4} (ab) - lo g_{4} (c d)

lo g_{4} (ab) = lo g_{4} (a) + lo g_{4} (b)

lo g_{4} (c d) = lo g_{4} (c) + lo g_{4} (d)

= lo g_{4} (a) + lo g_{4} (b) - (lo g_{4} (c) + lo g_{4} (d))

Apply the distributive law:

- (a + b) = - a - b

- (lo g_{4} (c) + lo g_{4} (d)) = - lo g_{4} (c) - lo g_{4} (d)

= lo g_{4} (a) + lo g_{4} (b) - lo g_{4} (c) - lo g_{4} (d)

ln (x - 2) - ln (2 x - 3)

lo g_{10} (5 x) - 7 (10 x - 2)

ln (\frac{6 x}{x ^{2} - 4})

lo g_{5} (4) + lo g_{5} (10)

lo g_{10} (18) - lo g_{10} (2)

What is log_{4}((ab)/(cd)) ?
The solution to log_{4}((ab)/(cd)) is log_{4}(a)+log_{4}(b)-log_{4}(c)-log_{4}(d)