What is expand log_{5}((x^2y)^6) ?

The solution to expand log_{5}((x^2y)^6) is 12log_{5}(x)+6log_{5}(y)

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expand log_{5}((x^2y)^6)

expand

lo g_{5} ((x^{2} y)^{6})

12 lo g_{5} (x) + 6 lo g_{5} (y)

Solution steps

lo g_{5} ((x^{2} y)^{6})

Apply log rule:

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

lo g_{5} ((x^{2} y)^{6}) = 6 lo g_{5} (x^{2} y)

= 6 lo g_{5} (x^{2} y)

Apply log rule:

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

6 lo g_{5} (x^{2} y) = 6 lo g_{5} (x^{2}) + 6 lo g_{5} (y)

= 6 lo g_{5} (x^{2}) + 6 lo g_{5} (y)

Apply log rule:

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

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

= 6 \cdot 2 lo g_{5} (x) + 6 lo g_{5} (y)

Multiply the numbers:

6 \cdot 2 = 12

= 12 lo g_{5} (x) + 6 lo g_{5} (y)

7 lo g_{3} (x) + 4 lo g_{3} (z) - 6 lo g_{3} (y)

lo g_{10} (\frac{1}{e ^{x}})

ln (\frac{270.5}{250}) (0.2872)

lo g_{10} (a) + 4 lo g_{10} (b) + 3 lo g_{10} (c)

lo g_{e} (x^{3} - 1) - lo g_{e} (x^{2} + x + 1)

What is expand log_{5}((x^2y)^6) ?
The solution to expand log_{5}((x^2y)^6) is 12log_{5}(x)+6log_{5}(y)