What is 2(log_{7}(x)+2log_{7}(y)-3log_{7}(z)) ?

The solution to 2(log_{7}(x)+2log_{7}(y)-3log_{7}(z)) is 2log_{7}((xy^2)/(z^3))

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simplify 2(log_{7}(x)+2log_{7}(y)-3log_{7}(z))

simplify

2 (lo g_{7} (x) + 2 lo g_{7} (y) - 3 lo g_{7} (z))

2 lo g_{7} (\frac{x y ^{2}}{z ^{3}})

Solution steps

2 (lo g_{7} (x) + 2 lo g_{7} (y) - 3 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}) - 3 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}) - 3 lo g_{7} (z))

Apply log rule:

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

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

= 2 (- lo g_{7} (z^{3}) + 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^{3}) = lo g_{7} (\frac{x y ^{2}}{z ^{3}})

= 2 lo g_{7} (\frac{x y ^{2}}{z ^{3}})

\frac{1}{2} lo g_{10} (\frac{y + 5}{y - 5})

3 ln (x) - 2 ln (2 x)

9.24 + lo g_{10} (\frac{0.21}{0.24})

lo g_{3} (b) + lo g_{3} (b + 9)

lo g_{10} (\frac{x}{z ^{2}})

What is 2(log_{7}(x)+2log_{7}(y)-3log_{7}(z)) ?
The solution to 2(log_{7}(x)+2log_{7}(y)-3log_{7}(z)) is 2log_{7}((xy^2)/(z^3))