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

The solution to expand log_{3}((x^2x^5)^3) is 21log_{3}(x)

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

expand

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

21 lo g_{3} (x)

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Multiply the numbers:

3 \cdot 2 = 6

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

Multiply the numbers:

3 \cdot 5 = 15

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

Add similar elements:

6 lo g_{3} (x) + 15 lo g_{3} (x) = 21 lo g_{3} (x)

= 21 lo g_{3} (x)

ln (1000 e^{- x})

ln (6.472 i)

ln (12) + \frac{1}{2} ln (7) - ln (2)

ln (- 2) - ln (- 5)

ln (- e^{- x} x)

What is expand log_{3}((x^2x^5)^3) ?
The solution to expand log_{3}((x^2x^5)^3) is 21log_{3}(x)