What is log_{3}(4)+2log_{3}(x)-log_{3}(5) ?

The solution to log_{3}(4)+2log_{3}(x)-log_{3}(5) is log_{3}((4x^2)/5)

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simplify log_{3}(4)+2log_{3}(x)-log_{3}(5)

simplify

lo g_{3} (4) + 2 lo g_{3} (x) - lo g_{3} (5)

lo g_{3} (\frac{4 x ^{2}}{5})

Solution steps

lo g_{3} (4) + 2 lo g_{3} (x) - lo g_{3} (5)

lo g_{3} (4) = 2 lo g_{3} (2)

= 2 lo g_{3} (2) + 2 lo g_{3} (x) - lo g_{3} (5)

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

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

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

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

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

Simplify

\frac{2 ^{2} x ^{2}}{5} : \frac{4 x ^{2}}{5}

= lo g_{3} (\frac{4 x ^{2}}{5})

∣ x - 4 ∣ + 2 ∣ x - 1 ∣ \geq 5

x + 4 = 0

x^{\frac{- 3}{2}} + 2 x^{\frac{- 1}{2}} + x^{\frac{1}{2}}

(x - 2)^{2} = - 5 x - 8

\frac{1}{2} - \frac{3}{2}

What is log_{3}(4)+2log_{3}(x)-log_{3}(5) ?
The solution to log_{3}(4)+2log_{3}(x)-log_{3}(5) is log_{3}((4x^2)/5)