What is log_{4}(x^2)+log_{4}(x) ?

The solution to log_{4}(x^2)+log_{4}(x) is 3log_{4}(x)

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simplify log_{4}(x^2)+log_{4}(x)

simplify

lo g_{4} (x^{2}) + lo g_{4} (x)

3 lo g_{4} (x)

Solution steps

lo g_{4} (x^{2}) + lo g_{4} (x)

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

lo g_{4} (x^{2}) + lo g_{4} (x) = lo g_{4} (x^{2} x)

= lo g_{4} (x^{2} x)

Simplify

x^{2} x : x^{3}

= lo g_{4} (x^{3})

Apply log rule

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

lo g_{4} (x^{3}) = 3 lo g_{4} (x)

= 3 lo g_{4} (x)

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

lo g_{10} (\frac{z ^{5}}{x ^{3} y})

2 lo g_{4} (3) + lo g_{4} (2)

ln (\frac{1}{4 9 ^{k}})

lo g_{8} (\frac{8}{x})

What is log_{4}(x^2)+log_{4}(x) ?
The solution to log_{4}(x^2)+log_{4}(x) is 3log_{4}(x)