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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

2 ln (x) + 4 ln (y) - 5 ln (z)

lo g_{4} (5 x y)

lo g_{b} (x^{2} y^{3})

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

lo g_{6} (\frac{1}{z ^{3}})

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