What is 1/5 log_{7}(x)+6log_{7}(w)-log_{7}(z) ?

The solution to 1/5 log_{7}(x)+6log_{7}(w)-log_{7}(z) is log_{7}((\sqrt[5]{x}w^6)/z)

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simplify 1/5 log_{7}(x)+6log_{7}(w)-log_{7}(z)

simplify

\frac{1}{5} lo g_{7} (x) + 6 lo g_{7} (w) - lo g_{7} (z)

Solution steps

\frac{1}{5} lo g_{7} (x) + 6 lo g_{7} (w) - lo g_{7} (z)

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

6 lo g_{7} (w) = lo g_{7} (w^{6})

= lo g_{7} (x^{\frac{1}{5}}) + lo g_{7} (w^{6}) - lo g_{7} (z)

Apply log rule:

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

lo g_{7} (x^{\frac{1}{5}}) + lo g_{7} (w^{6}) = lo g_{7} (x^{\frac{1}{5}} w^{6})

= lo g_{7} (x^{\frac{1}{5}} w^{6}) - lo g_{7} (z)

Apply log rule:

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

lo g_{7} (x^{\frac{1}{5}} w^{6}) - lo g_{7} (z) = lo g_{7} (\frac{x ^{\frac{1}{5}} w ^{6}}{z})

= lo g_{7} (\frac{x ^{\frac{1}{5}} w ^{6}}{z})

Apply exponent rule:

lo g_{\frac{1}{2}} (\frac{3 x ^{2}}{2})

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

\frac{lo g _{10} ( a ) + lo g _{10} ( b )}{lo g _{10} ( a ) lo g _{10} ( b )}

lo g_{4} (5) + lo g_{4} (7)

What is 1/5 log_{7}(x)+6log_{7}(w)-log_{7}(z) ?
The solution to 1/5 log_{7}(x)+6log_{7}(w)-log_{7}(z) is log_{7}((\sqrt[5]{x}w^6)/z)