What is log_{2}(a/(b^2)) ?

The solution to log_{2}(a/(b^2)) is log_{2}(a)-2log_{2}(b)

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simplify log_{2}(a/(b^2))

simplify

lo g_{2} (\frac{a}{b ^{2}})

lo g_{2} (a) - 2 lo g_{2} (b)

Solution steps

lo g_{2} (\frac{a}{b ^{2}})

Apply log rule:

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

lo g_{2} (\frac{a}{b ^{2}}) = lo g_{2} (a) - lo g_{2} (b^{2})

= lo g_{2} (a) - lo g_{2} (b^{2})

Simplify

lo g_{2} (b^{2}) : 2 lo g_{2} (b)

= lo g_{2} (a) - 2 lo g_{2} (b)

lo g_{4} (5 x)

lo g_{5} (4) + \frac{1}{3} lo g_{5} (x)

ln (\frac{6}{5})

\frac{15}{2} ln (\frac{2}{5})

\frac{3}{2} [ln (x^{2} - 1) - ln (x + 1) + ln (x - 1)]

What is log_{2}(a/(b^2)) ?
The solution to log_{2}(a/(b^2)) is log_{2}(a)-2log_{2}(b)