What is log_{b}(\sqrt[3]{3b}) ?

The solution to log_{b}(\sqrt[3]{3b}) is (log_{b}(3)+1)/3

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simplify log_{b}(\sqrt[3]{3b})

simplify

\frac{lo g _{b} ( 3 ) + 1}{3}

Solution steps

Simplify

= lo g_{b} (3^{\frac{1}{3}} b^{\frac{1}{3}})

Apply log rule:

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

lo g_{b} (3^{\frac{1}{3}} b^{\frac{1}{3}}) = lo g_{b} (3^{\frac{1}{3}}) + lo g_{b} (b^{\frac{1}{3}})

= lo g_{b} (3^{\frac{1}{3}}) + lo g_{b} (b^{\frac{1}{3}})

Apply log rule:

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

lo g_{b} (3^{\frac{1}{3}}) = \frac{1}{3} lo g_{b} (3)

= \frac{1}{3} lo g_{b} (3) + lo g_{b} (b^{\frac{1}{3}})

Apply log rule:

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

lo g_{b} (b^{\frac{1}{3}}) = \frac{1}{3}

= \frac{1}{3} lo g_{b} (3) + \frac{1}{3}

Simplify

\frac{1}{3} lo g_{b} (3) : \frac{lo g _{b} ( 3 )}{3}

= \frac{lo g _{b} ( 3 )}{3} + \frac{1}{3}

Join

\frac{lo g _{b} ( 3 )}{3} + \frac{1}{3} : \frac{lo g _{b} ( 3 ) + 1}{3}

= \frac{lo g _{b} ( 3 ) + 1}{3}

\frac{x + 1}{- x + 5} > 0

4 x + 1 = 5 x - 2

2 lo g_{3} (4) - lo g_{3} (48)

- \frac{3 y}{12} - \frac{6 y}{12} - \frac{y}{8} = - \frac{1}{4}

4.75 x = 24.7

What is log_{b}(\sqrt[3]{3b}) ?
The solution to log_{b}(\sqrt[3]{3b}) is (log_{b}(3)+1)/3