What is 2(log_{7}(x)+2log_{7}(y)-4log_{7}(z)) ?

The solution to 2(log_{7}(x)+2log_{7}(y)-4log_{7}(z)) is 2log_{7}((xy^2)/(z^4))

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simplify 2(log_{7}(x)+2log_{7}(y)-4log_{7}(z))

simplify

2 (lo g_{7} (x) + 2 lo g_{7} (y) - 4 lo g_{7} (z))

2 lo g_{7} (\frac{x y ^{2}}{z ^{4}})

Solution steps

2 (lo g_{7} (x) + 2 lo g_{7} (y) - 4 lo g_{7} (z))

Apply log rule:

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

2 lo g_{7} (y) = lo g_{7} (y^{2})

= 2 (lo g_{7} (x) + lo g_{7} (y^{2}) - 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^{2}) = lo g_{7} (x y^{2})

= 2 (lo g_{7} (x y^{2}) - 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})

= 2 (- lo g_{7} (z^{4}) + lo g_{7} (x y^{2}))

Apply log rule:

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

lo g_{7} (x y^{2}) - lo g_{7} (z^{4}) = lo g_{7} (\frac{x y ^{2}}{z ^{4}})

= 2 lo g_{7} (\frac{x y ^{2}}{z ^{4}})

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What is 2(log_{7}(x)+2log_{7}(y)-4log_{7}(z)) ?
The solution to 2(log_{7}(x)+2log_{7}(y)-4log_{7}(z)) is 2log_{7}((xy^2)/(z^4))