What is log_{4}(y-1)+log_{4}(x/2) ?

The solution to log_{4}(y-1)+log_{4}(x/2) is log_{4}((x(y-1))/2)

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simplify log_{4}(y-1)+log_{4}(x/2)

simplify

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

lo g_{4} (\frac{x ( y - 1 )}{2})

Solution steps

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

Apply log rule:

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

lo g_{4} (y - 1) + lo g_{4} (\frac{x}{2}) = lo g_{4} ((y - 1) \frac{x}{2})

= lo g_{4} ((y - 1) \frac{x}{2})

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= lo g_{4} (\frac{x ( y - 1 )}{2})

ln (\frac{2 x + 1}{1 - x})

ln (\frac{2 x}{x})

lo g_{5} (\frac{125}{x + 6})

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

\frac{1}{3} lo g_{10} (x) - 6 lo g_{10} (sin (3 x)) + 2

What is log_{4}(y-1)+log_{4}(x/2) ?
The solution to log_{4}(y-1)+log_{4}(x/2) is log_{4}((x(y-1))/2)