What is 2(log_{7}(x)+3log_{7}(y)-4log_{7}(z)) ?

The solution to 2(log_{7}(x)+3log_{7}(y)-4log_{7}(z)) is 2log_{7}((xy^3)/(z^4))

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simplify 2(log_{7}(x)+3log_{7}(y)-4log_{7}(z))

simplify

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

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

Solution steps

2 (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})

= 2 (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})

= 2 (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})

= 2 (- 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}})

= 2 lo g_{7} (\frac{x y ^{3}}{z ^{4}})

lo g_{3} (\frac{27 b ^{3} y ^{2} - 3}{y ( x + 3 ) ^{2}})

lo g_{10} (x) + 3 lo g_{10} (y) - 3 lo g_{10} (z)

ln^{2} (- 1) + 2 ln (- 1)

ln (\frac{x ^{p} e ^{(- y)}}{z})

lo g_{10} (\frac{a ^{3} b ^{3}}{c ^{4}})

What is 2(log_{7}(x)+3log_{7}(y)-4log_{7}(z)) ?
The solution to 2(log_{7}(x)+3log_{7}(y)-4log_{7}(z)) is 2log_{7}((xy^3)/(z^4))