What is 3log_{7}(x)-4log_{7}(y) ?

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

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simplify 3log_{7}(x)-4log_{7}(y)

simplify

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

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

Solution steps

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

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

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

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

ln (\frac{6.09}{9.42 \cdot 1 0 ^{- 3}}) \cdot 0.0002

ln (\frac{249}{3999})

ln (500) + 3 ln (\frac{575}{500})

ln (\frac{2 t ^{2} - t - 6}{t + 1})

ln (x^{a} y^{b})

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