What is 8log_{b}(x)+9log_{b}(y)-4log_{b}(z) ?

The solution to 8log_{b}(x)+9log_{b}(y)-4log_{b}(z) is log_{b}((x^8y^9)/(z^4))

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simplify 8log_{b}(x)+9log_{b}(y)-4log_{b}(z)

simplify

8 lo g_{b} (x) + 9 lo g_{b} (y) - 4 lo g_{b} (z)

lo g_{b} (\frac{x ^{8} y ^{9}}{z ^{4}})

Solution steps

8 lo g_{b} (x) + 9 lo g_{b} (y) - 4 lo g_{b} (z)

Apply log rule:

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

8 lo g_{b} (x) = lo g_{b} (x^{8})

= lo g_{b} (x^{8}) + 9 lo g_{b} (y) - 4 lo g_{b} (z)

Apply log rule:

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

9 lo g_{b} (y) = lo g_{b} (y^{9})

= lo g_{b} (x^{8}) + lo g_{b} (y^{9}) - 4 lo g_{b} (z)

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

lo g_{b} (x^{8}) + lo g_{b} (y^{9}) = lo g_{b} (x^{8} y^{9})

= lo g_{b} (x^{8} y^{9}) - 4 lo g_{b} (z)

Apply log rule:

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

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

= lo g_{b} (x^{8} y^{9}) - lo g_{b} (z^{4})

Apply log rule:

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

lo g_{b} (x^{8} y^{9}) - lo g_{b} (z^{4}) = lo g_{b} (\frac{x ^{8} y ^{9}}{z ^{4}})

= lo g_{b} (\frac{x ^{8} y ^{9}}{z ^{4}})

\frac{23}{2} (2 \cdot ln (\frac{a ^{3}}{b}) + 22 \cdot ln (\frac{1}{b}))

ln (\frac{2}{25}) - ln (\frac{2}{4})

5 ln ∣ x - 1 ∣ - ln ∣ x ∣

\frac{1}{3} ln ∣ tan (x) + sec (x) ∣

ln (sinh (x) \cdot cosh (x))

What is 8log_{b}(x)+9log_{b}(y)-4log_{b}(z) ?
The solution to 8log_{b}(x)+9log_{b}(y)-4log_{b}(z) is log_{b}((x^8y^9)/(z^4))