What is simplify-3log_{7}(x)+5log_{7}(y)-log_{3}(z) ?

The solution to simplify-3log_{7}(x)+5log_{7}(y)-log_{3}(z) is log_{7}((y^5)/(x^3))-log_{3}(z)

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simplify-3log_{7}(x)+5log_{7}(y)-log_{3}(z)

simplify

- 3 lo g_{7} (x) + 5 lo g_{7} (y) - lo g_{3} (z)

lo g_{7} (\frac{y ^{5}}{x ^{3}}) - lo g_{3} (z)

Solution steps

- 3 lo g_{7} (x) + 5 lo g_{7} (y) - lo g_{3} (z)

Apply log rule:

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

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

= - lo g_{7} (x^{3}) + 5 lo g_{7} (y) - lo g_{3} (z)

Apply log rule:

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

5 lo g_{7} (y) = lo g_{7} (y^{5})

= - lo g_{7} (x^{3}) + lo g_{7} (y^{5}) - lo g_{3} (z)

Apply log rule:

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

lo g_{7} (y^{5}) - lo g_{7} (x^{3}) = lo g_{7} (\frac{y ^{5}}{x ^{3}})

= lo g_{7} (\frac{y ^{5}}{x ^{3}}) - lo g_{3} (z)

14 + lo g_{10} (\frac{0.00084}{48})

ln (7 x^{2} - 1) - ln (x^{2})

x^{2} + 1 - ln (\frac{1 + x ^{2} + 1}{x})

\frac{1}{2} ln ∣ x - 3 ∣ - \frac{1}{x - 3} + \frac{1}{2} ln ∣ x + 3 ∣ + C

ln (5) + 3 ln (4) - ln (8)

What is simplify-3log_{7}(x)+5log_{7}(y)-log_{3}(z) ?
The solution to simplify-3log_{7}(x)+5log_{7}(y)-log_{3}(z) is log_{7}((y^5)/(x^3))-log_{3}(z)