What is 2log_{a}(y/z) ?

The solution to 2log_{a}(y/z) is 2log_{a}(y)-2log_{a}(z)

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simplify 2log_{a}(y/z)

simplify

2 lo g_{a} (\frac{y}{z})

2 lo g_{a} (y) - 2 lo g_{a} (z)

Solution steps

2 lo g_{a} (\frac{y}{z})

Apply log rule:

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

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

= 2 (lo g_{a} (y) - lo g_{a} (z))

Apply the distributive law:

a (b - c) = ab - a c

2 (lo g_{a} (y) - lo g_{a} (z)) = 2 lo g_{a} (y) - 2 lo g_{a} (z)

= 2 lo g_{a} (y) - 2 lo g_{a} (z)

lo g_{10} ((\frac{6}{11})^{5})

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

lo g_{2} (\frac{27}{3}) - lo g_{2} (\frac{16}{2})

ln (2 x)

lo g_{5} (\frac{x}{25})

What is 2log_{a}(y/z) ?
The solution to 2log_{a}(y/z) is 2log_{a}(y)-2log_{a}(z)