What is 1/5 log_{a}(x)+7log_{a}(y)-log_{a}(z) ?

The solution to 1/5 log_{a}(x)+7log_{a}(y)-log_{a}(z) is log_{a}((\sqrt[5]{x}y^7)/z)

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simplify 1/5 log_{a}(x)+7log_{a}(y)-log_{a}(z)

simplify

\frac{1}{5} lo g_{a} (x) + 7 lo g_{a} (y) - lo g_{a} (z)

Solution steps

\frac{1}{5} lo g_{a} (x) + 7 lo g_{a} (y) - lo g_{a} (z)

\frac{1}{5} lo g_{a} (x) = lo g_{a} (x^{\frac{1}{5}})

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

= lo g_{a} (x^{\frac{1}{5}}) + lo g_{a} (y^{7}) - lo g_{a} (z)

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

lo g_{a} (x^{\frac{1}{5}}) + lo g_{a} (y^{7}) = lo g_{a} (x^{\frac{1}{5}} y^{7})

= lo g_{a} (x^{\frac{1}{5}} y^{7}) - lo g_{a} (z)

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{a} (x^{\frac{1}{5}} y^{7}) - lo g_{a} (z) = lo g_{a} (\frac{x ^{\frac{1}{5}} y ^{7}}{z})

= lo g_{a} (\frac{x ^{\frac{1}{5}} y ^{7}}{z})

Apply exponent rule:

∣ 3 x + 5 ∣ \geq 2

3^{2} + 4

∣ 2 x + 3 ∣ \geq - 11

2 x^{5} - 32 x

x (5 + 12 x) = 28

What is 1/5 log_{a}(x)+7log_{a}(y)-log_{a}(z) ?
The solution to 1/5 log_{a}(x)+7log_{a}(y)-log_{a}(z) is log_{a}((\sqrt[5]{x}y^7)/z)