What is 2log_{5}(5x^3)+1/3 log_{5}(x^2+6) ?

The solution to 2log_{5}(5x^3)+1/3 log_{5}(x^2+6) is log_{5}(25x^6\sqrt[3]{x^2+6})

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simplify 2log_{5}(5x^3)+1/3 log_{5}(x^2+6)

simplify

2 lo g_{5} (5 x^{3}) + \frac{1}{3} lo g_{5} (x^{2} + 6)

Solution steps

2 lo g_{5} (5 x^{3}) + \frac{1}{3} lo g_{5} (x^{2} + 6)

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

\frac{1}{3} lo g_{5} (x^{2} + 6) = lo g_{5} ((x^{2} + 6)^{\frac{1}{3}})

= lo g_{5} ((5 x^{3})^{2}) + lo g_{5} ((x^{2} + 6)^{\frac{1}{3}})

Apply log rule:

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

lo g_{5} ((5 x^{3})^{2}) + lo g_{5} ((x^{2} + 6)^{\frac{1}{3}}) = lo g_{5} ((5 x^{3})^{2} (x^{2} + 6)^{\frac{1}{3}})

= lo g_{5} ((5 x^{3})^{2} (x^{2} + 6)^{\frac{1}{3}})

Simplify

(5 x^{3})^{2} : 25 x^{6}

= lo g_{5} (25 x^{6} (x^{2} + 6)^{\frac{1}{3}})

Apply exponent rule:

\frac{7}{5} = \frac{x}{7}

(x + 1) (x + 1) = 1

5 x^{2} + 470 = - 100 x

3 ∣ 2 x - 7 ∣ = 3

\frac{3 X + 2}{X - 1} > 0

What is 2log_{5}(5x^3)+1/3 log_{5}(x^2+6) ?
The solution to 2log_{5}(5x^3)+1/3 log_{5}(x^2+6) is log_{5}(25x^6\sqrt[3]{x^2+6})