What is 2log_{3}(x)+log_{3}(a) ?

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

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simplify 2log_{3}(x)+log_{3}(a)

simplify

2 lo g_{3} (x) + lo g_{3} (a)

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

Solution steps

2 lo g_{3} (x) + lo g_{3} (a)

Apply log rule:

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

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

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

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

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

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

\frac{1}{6} ((ln ∣ 1 - 3 ∣ - ln ∣ 0 - 3 ∣) - (ln ∣ 1 + 3 ∣ - ln ∣ 0 + 3 ∣))

- lo g_{10} (6.38 \cdot 1 0^{- 6})

\frac{1}{6} [5 ln (x + 9) - ln (x) - ln (x^{2} - 4)]

\frac{1}{3} (ln (5) - ln (7))

3.74 + lo g_{10} (\frac{40 + 5 x}{60 - 5 x})

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