What is expand log_{b}(((x^4)/(y^3z^2))^{-5}) ?

The solution to expand log_{b}(((x^4)/(y^3z^2))^{-5}) is -5(4log_{b}(x)-log_{b}(y^3z^2))

Popular >

expand log_{b}(((x^4)/(y^3z^2))^{-5})

expand

lo g_{b} ((\frac{x ^{4}}{y ^{3} z ^{2}})^{- 5})

- 5 (4 lo g_{b} (x) - lo g_{b} (y^{3} z^{2}))

Solution steps

lo g_{b} ((\frac{x ^{4}}{y ^{3} z ^{2}})^{- 5})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{b} ((\frac{x ^{4}}{y ^{3} z ^{2}})^{- 5}) = - 5 lo g_{b} (\frac{x ^{4}}{y ^{3} z ^{2}})

= - 5 lo g_{b} (\frac{x ^{4}}{y ^{3} z ^{2}})

Apply log rule:

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

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

= - 5 (lo g_{b} (x^{4}) - lo g_{b} (y^{3} z^{2}))

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{b} (x^{4}) = 4 lo g_{b} (x)

= - 5 (4 lo g_{b} (x) - lo g_{b} (y^{3} z^{2}))

- lo g_{10} (7.1 \cdot 1 0^{- 10})

lo g_{a} (x) - 3 lo g_{a} (x - y) - \frac{1}{2} lo g_{a} (x)

lo g_{6} (\frac{x ^{7} ( x + 9 )}{( x - 4 ) ^{5}})

ln (x^{2} (x + 6)^{7} (x^{2} + 5)^{4})

1004 \cdot ln (\frac{100}{930}) - 287 \cdot ln (\frac{3}{4})

What is expand log_{b}(((x^4)/(y^3z^2))^{-5}) ?
The solution to expand log_{b}(((x^4)/(y^3z^2))^{-5}) is -5(4log_{b}(x)-log_{b}(y^3z^2))