What is log_{3}(6)+2log_{3}(x)+1/2 log_{3}(9) ?

The solution to log_{3}(6)+2log_{3}(x)+1/2 log_{3}(9) is log_{3}(18x^2)

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simplify log_{3}(6)+2log_{3}(x)+1/2 log_{3}(9)

simplify

lo g_{3} (6) + 2 lo g_{3} (x) + \frac{1}{2} lo g_{3} (9)

lo g_{3} (18 x^{2})

Solution steps

lo g_{3} (6) + 2 lo g_{3} (x) + \frac{1}{2} lo g_{3} (9)

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

\frac{1}{2} lo g_{3} (9) = lo g_{3} (9^{\frac{1}{2}})

= lo g_{3} (6) + lo g_{3} (x^{2}) + lo g_{3} (9^{\frac{1}{2}})

Apply log rule:

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

lo g_{3} (6) + lo g_{3} (x^{2}) = lo g_{3} (6 x^{2})

= lo g_{3} (6 x^{2}) + lo g_{3} (9^{\frac{1}{2}})

Apply log rule:

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

lo g_{3} (6 x^{2}) + lo g_{3} (9^{\frac{1}{2}}) = lo g_{3} (6 x^{2} \cdot 9^{\frac{1}{2}})

= lo g_{3} (6 x^{2} \cdot 9^{\frac{1}{2}})

Simplify

6 x^{2} \cdot 9^{\frac{1}{2}} : 18 x^{2}

= lo g_{3} (18 x^{2})

lo g_{10} (x) + lo g_{10} (y) + lo g_{10} (2 z)

lo g_{10} (\frac{x}{100 y ^{4}})

5 lo g_{b} (q) + 2 lo g_{b} (y)

- 0.35 lo g_{2} (0.35) - 0.65 lo g_{2} (0.65)

5 lo g_{b} (q) - lo g_{b} (r)

What is log_{3}(6)+2log_{3}(x)+1/2 log_{3}(9) ?
The solution to log_{3}(6)+2log_{3}(x)+1/2 log_{3}(9) is log_{3}(18x^2)