What is 2log_{2}(x)+log_{2}(x+2) ?

The solution to 2log_{2}(x)+log_{2}(x+2) is log_{2}(x^2(x+2))

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simplify 2log_{2}(x)+log_{2}(x+2)

simplify

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

lo g_{2} (x^{2} (x + 2))

Solution steps

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

Apply log rule:

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

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

= lo g_{2} (x^{2}) + lo g_{2} (x + 2)

Apply log rule:

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

lo g_{2} (x^{2}) + lo g_{2} (x + 2) = lo g_{2} (x^{2} (x + 2))

= lo g_{2} (x^{2} (x + 2))

lo g_{10} (\frac{x ^{2} - c ^{2}}{2}) - lo g_{10} (x - c)

2 ln (3) - \frac{1}{2} ln (2) + \frac{π}{12}

lo g_{10} (\frac{x ^{2}}{7})

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

What is 2log_{2}(x)+log_{2}(x+2) ?
The solution to 2log_{2}(x)+log_{2}(x+2) is log_{2}(x^2(x+2))