What is expand log_{3}((x^2y^5)^3) ?

The solution to expand log_{3}((x^2y^5)^3) is 6log_{3}(x)+15log_{3}(y)

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expand log_{3}((x^2y^5)^3)

expand

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

6 lo g_{3} (x) + 15 lo g_{3} (y)

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

= 3 \cdot 2 lo g_{3} (x) + 3 lo g_{3} (y^{5})

Apply log rule:

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

lo g_{3} (y^{5}) = 5 lo g_{3} (y)

= 3 \cdot 2 lo g_{3} (x) + 3 \cdot 5 lo g_{3} (y)

Multiply the numbers:

3 \cdot 2 = 6

= 6 lo g_{3} (x) + 3 \cdot 5 lo g_{3} (y)

Multiply the numbers:

3 \cdot 5 = 15

= 6 lo g_{3} (x) + 15 lo g_{3} (y)

\frac{1}{2} ln (x + 1) - ln (2 x + 1)

ln (\frac{20}{40})

ln ∣ x + 2 ∣ + ln ∣ x - 2 ∣

lo g_{9} (\frac{c}{81})

2 ln ∣ x ∣ + 2 ln ∣ x - 3 ∣

What is expand log_{3}((x^2y^5)^3) ?
The solution to expand log_{3}((x^2y^5)^3) is 6log_{3}(x)+15log_{3}(y)