What is 2log_{2}(a)+2log_{2}(b)-2log_{2}(a+b) ?

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

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simplify 2log_{2}(a)+2log_{2}(b)-2log_{2}(a+b)

simplify

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

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

Solution steps

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

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

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

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

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

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

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

4.35 + lo g_{10} (\frac{2}{3})

lo g_{2} (\frac{e ^{7 x}}{e ^{8 y}})

2 lo g_{5} (1.75) + lo g_{5} (16)

lo g_{e} (\frac{14}{121})

- ln (\frac{22}{78})

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