What is 5log_{b}(x^2)+log_{b}(sqrt(x)) ?

The solution to 5log_{b}(x^2)+log_{b}(sqrt(x)) is log_{b}(x^{10}sqrt(x))

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simplify 5log_{b}(x^2)+log_{b}(sqrt(x))

simplify

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

lo g_{b} (x^{10} x)

Solution steps

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

Apply log rule:

b \cdot lo g_{a} (x) = lo g_{a} (x^{b})

5 lo g_{b} (x^{2}) = lo g_{b} ((x^{2})^{5})

= lo g_{b} ((x^{2})^{5}) + lo g_{b} (x)

Apply log rule:

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

lo g_{b} ((x^{2})^{5}) + lo g_{b} (x) = lo g_{b} ((x^{2})^{5} x)

= lo g_{b} ((x^{2})^{5} x)

Simplify

(x^{2})^{5} : x^{10}

= lo g_{b} (x^{10} x)

lo g_{4} (9^{3})

lo g_{10} (\frac{x y ^{4}}{z ^{5}})

lo g_{10} (\frac{p ^{3} + q}{1000})

lo g_{4} (\frac{x ^{2}}{5})

ln (x^{7}) - ln (x)

What is 5log_{b}(x^2)+log_{b}(sqrt(x)) ?
The solution to 5log_{b}(x^2)+log_{b}(sqrt(x)) is log_{b}(x^{10}sqrt(x))