What is log_{7}(x^5)-5log_{7}(x^2) ?

The solution to log_{7}(x^5)-5log_{7}(x^2) is -5log_{7}(x)

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simplify log_{7}(x^5)-5log_{7}(x^2)

simplify

lo g_{7} (x^{5}) - 5 lo g_{7} (x^{2})

- 5 lo g_{7} (x)

Solution steps

lo g_{7} (x^{5}) - 5 lo g_{7} (x^{2})

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), assuming x > 0

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

= 5 lo g_{7} (x) - 5 lo g_{7} (x^{2})

Simplify

- 5 lo g_{7} (x^{2}) : - 10 lo g_{7} (x)

= 5 lo g_{7} (x) - 10 lo g_{7} (x)

Add similar elements:

5 lo g_{7} (x) - 10 lo g_{7} (x) = - 5 lo g_{7} (x)

= - 5 lo g_{7} (x)

lo g_{5} (\frac{9 x}{y ^{3}})

lo g_{c} (x^{7} y^{6} z)

lo g_{4} (2 x) + lo g_{4} (8 y)

lo g_{10} (x y^{8})

- lo g_{e} (0.917) - lo g_{e} (0.964)

What is log_{7}(x^5)-5log_{7}(x^2) ?
The solution to log_{7}(x^5)-5log_{7}(x^2) is -5log_{7}(x)