What is expand log_{3}((2x)^2) ?

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

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expand log_{3}((2x)^2)

expand

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

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

Solution steps

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

Apply log rule:

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

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

= 2 lo g_{3} (2 x)

Apply log rule:

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

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

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

ln (\frac{1}{a b ^{3}})

ln ((\frac{2}{a ^{3}})^{4})

lo g_{10} (\frac{a ^{4}}{b ^{2} c ^{3}})

ln (θ (θ + 1) x^{θ - 1} (1 - x))

300 ln (\frac{1}{2})

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