What is log_{2}(x^2)+log_{2}(x^3) ?

The solution to log_{2}(x^2)+log_{2}(x^3) is 5log_{2}(x)

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simplify log_{2}(x^2)+log_{2}(x^3)

simplify

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

5 lo g_{2} (x)

Solution steps

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

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), assuming x > 0

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

= 2 lo g_{2} (x) + lo g_{2} (x^{3})

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), assuming x > 0

lo g_{2} (x^{3}) = 3 lo g_{2} (x)

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

Add similar elements:

2 lo g_{2} (x) + 3 lo g_{2} (x) = 5 lo g_{2} (x)

= 5 lo g_{2} (x)

lo g_{2} (8 a)

ln (\frac{x + 3}{x - 3})

\frac{1}{4} lo g_{2} (\frac{1}{4}) + \frac{3}{4} lo g_{2} (\frac{3}{4})

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

ln (\frac{1}{x})

What is log_{2}(x^2)+log_{2}(x^3) ?
The solution to log_{2}(x^2)+log_{2}(x^3) is 5log_{2}(x)