What is expand log_{7}(((x^5)/y)^5) ?

The solution to expand log_{7}(((x^5)/y)^5) is 5(5log_{7}(x)-log_{7}(y))

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expand log_{7}(((x^5)/y)^5)

expand

lo g_{7} ((\frac{x ^{5}}{y})^{5})

5 (5 lo g_{7} (x) - lo g_{7} (y))

Solution steps

lo g_{7} ((\frac{x ^{5}}{y})^{5})

Apply log rule:

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

lo g_{7} ((\frac{x ^{5}}{y})^{5}) = 5 lo g_{7} (\frac{x ^{5}}{y})

= 5 lo g_{7} (\frac{x ^{5}}{y})

Apply log rule:

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

lo g_{7} (\frac{x ^{5}}{y}) = lo g_{7} (x^{5}) - lo g_{7} (y)

= 5 (lo g_{7} (x^{5}) - lo g_{7} (y))

Apply log rule:

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

lo g_{7} (x^{5}) = 5 lo g_{7} (x)

= 5 (5 lo g_{7} (x) - lo g_{7} (y))

ln (x ln (x))

lo g_{10} (7) - lo g_{10} (x)

lo g_{10} (2) + lo g_{10} (p)

3 lo g_{10} (3) + lo g_{10} (x) - lo g_{10} (3 x)

lo g_{10} (7) - lo g_{10} (4)

What is expand log_{7}(((x^5)/y)^5) ?
The solution to expand log_{7}(((x^5)/y)^5) is 5(5log_{7}(x)-log_{7}(y))