What is expand log_{7}((xyz^2)^3) ?

The solution to expand log_{7}((xyz^2)^3) is 3log_{7}(x)+3log_{7}(y)+6log_{7}(z)

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expand log_{7}((xyz^2)^3)

expand

lo g_{7} ((x y z^{2})^{3})

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

Solution steps

lo g_{7} ((x y z^{2})^{3})

Apply log rule:

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

lo g_{7} ((x y z^{2})^{3}) = 3 lo g_{7} (x y z^{2})

= 3 lo g_{7} (x y z^{2})

Apply log rule:

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

3 lo g_{7} (x y z^{2}) = 3 lo g_{7} (x) + 3 lo g_{7} (y) + 3 lo g_{7} (z^{2})

= 3 lo g_{7} (x) + 3 lo g_{7} (y) + 3 lo g_{7} (z^{2})

Apply log rule:

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

lo g_{7} (z^{2}) = 2 lo g_{7} (z)

= 3 lo g_{7} (x) + 3 lo g_{7} (y) + 3 \cdot 2 lo g_{7} (z)

Multiply the numbers:

3 \cdot 2 = 6

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

5 ln ∣ x + 3 ∣ - \frac{8}{x + 3} + 5 ln ∣ x + 7 ∣

ln (e^{x} \cdot x)

lo g_{10} (\frac{g j ^{5} k}{100})

ln (\frac{5}{2})

3 ln ∣ x ∣ - 2 ln ∣ x + 1 ∣ + \frac{8}{x + 1} + C

What is expand log_{7}((xyz^2)^3) ?
The solution to expand log_{7}((xyz^2)^3) is 3log_{7}(x)+3log_{7}(y)+6log_{7}(z)