What is expand log_{7}((x^3)/(y^4)) ?

The solution to expand log_{7}((x^3)/(y^4)) is 3log_{7}(x)-4log_{7}(y)

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expand log_{7}((x^3)/(y^4))

expand

lo g_{7} (\frac{x ^{3}}{y ^{4}})

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

Solution steps

lo g_{7} (\frac{x ^{3}}{y ^{4}})

Apply log rule:

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

lo g_{7} (\frac{x ^{3}}{y ^{4}}) = lo g_{7} (x^{3}) - lo g_{7} (y^{4})

= lo g_{7} (x^{3}) - lo g_{7} (y^{4})

Apply log rule:

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

lo g_{7} (x^{3}) = 3 lo g_{7} (x)

= 3 lo g_{7} (x) - lo g_{7} (y^{4})

Apply log rule:

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

lo g_{7} (y^{4}) = 4 lo g_{7} (y)

= 3 lo g_{7} (x) - 4 lo g_{7} (y)

ln (\frac{a b ^{3}}{c d ^{3}})

lo g_{0.4} (\frac{3}{2}) - lo g_{2.5} (2)

lo g_{10} (\frac{z ^{4}}{x ^{5} y})

lo g_{2} (\frac{4}{y}) 5

lo g_{10} (\frac{u ^{2} + v ^{2}}{10000})

What is expand log_{7}((x^3)/(y^4)) ?
The solution to expand log_{7}((x^3)/(y^4)) is 3log_{7}(x)-4log_{7}(y)