What is simplify-20log_{4}(x)-80log_{4}(y) ?

The solution to simplify-20log_{4}(x)-80log_{4}(y) is -log_{4}(x^{20}y^{80})

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simplify-20log_{4}(x)-80log_{4}(y)

simplify

- 20 lo g_{4} (x) - 80 lo g_{4} (y)

- lo g_{4} (x^{20} y^{80})

Solution steps

- 20 lo g_{4} (x) - 80 lo g_{4} (y)

Apply log rule:

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

20 lo g_{4} (x) = lo g_{4} (x^{20})

= - lo g_{4} (x^{20}) - 80 lo g_{4} (y)

Apply log rule:

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

80 lo g_{4} (y) = lo g_{4} (y^{80})

= - lo g_{4} (x^{20}) - lo g_{4} (y^{80})

Rewrite

- lo g_{4} (x^{20}) - lo g_{4} (y^{80})

- (lo g_{4} (x^{20}) + lo g_{4} (y^{80}))

= - (lo g_{4} (x^{20}) + lo g_{4} (y^{80}))

Apply log rule:

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

lo g_{4} (x^{20}) + lo g_{4} (y^{80}) = lo g_{4} (x^{20} y^{80})

= - lo g_{4} (x^{20} y^{80})

\frac{1}{3} lo g_{3} (8) - lo g_{3} (10) + 4 lo g_{3} (2)

lo g_{10} (2.5) + 0.4 lo g_{10} (x)

ln (\frac{30}{130})

lo g_{10} (m \cdot (\frac{p}{q}))

lo g_{10} (\frac{x}{10000 y ^{9}})

What is simplify-20log_{4}(x)-80log_{4}(y) ?
The solution to simplify-20log_{4}(x)-80log_{4}(y) is -log_{4}(x^{20}y^{80})