What is expand log_{7}(((x^6)/y)^4) ?

The solution to expand log_{7}(((x^6)/y)^4) is 4(6log_{7}(x)-log_{7}(y))

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expand log_{7}(((x^6)/y)^4)

expand

lo g_{7} ((\frac{x ^{6}}{y})^{4})

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

Solution steps

lo g_{7} ((\frac{x ^{6}}{y})^{4})

Apply log rule:

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

lo g_{7} ((\frac{x ^{6}}{y})^{4}) = 4 lo g_{7} (\frac{x ^{6}}{y})

= 4 lo g_{7} (\frac{x ^{6}}{y})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

lo g_{7} (\frac{x ^{6}}{y}) = lo g_{7} (x^{6}) - lo g_{7} (y)

= 4 (lo g_{7} (x^{6}) - lo g_{7} (y))

Apply log rule:

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

lo g_{7} (x^{6}) = 6 lo g_{7} (x)

= 4 (6 lo g_{7} (x) - lo g_{7} (y))

lo g_{10} (3 \cdot 11)

2 ln (x) + 5 ln (y)

ln (e^{9}) + ln (3 e^{8})

ln (x (x + 7))

- \frac{1}{2} ln ∣ u + 1 ∣ + \frac{1}{2} ln ∣ u - 1 ∣

What is expand log_{7}(((x^6)/y)^4) ?
The solution to expand log_{7}(((x^6)/y)^4) is 4(6log_{7}(x)-log_{7}(y))