What is 2log_{5}(x)+4(log_{5}(y)-2log_{5}(z)) ?

The solution to 2log_{5}(x)+4(log_{5}(y)-2log_{5}(z)) is log_{5}((x^2y^4)/(z^8))

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simplify 2log_{5}(x)+4(log_{5}(y)-2log_{5}(z))

simplify

2 lo g_{5} (x) + 4 (lo g_{5} (y) - 2 lo g_{5} (z))

lo g_{5} (\frac{x ^{2} y ^{4}}{z ^{8}})

Solution steps

2 lo g_{5} (x) + 4 (lo g_{5} (y) - 2 lo g_{5} (z))

Apply log rule:

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

2 lo g_{5} (z) = lo g_{5} (z^{2})

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

Apply log rule:

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

lo g_{5} (y) - lo g_{5} (z^{2}) = lo g_{5} (\frac{y}{z ^{2}})

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

Apply log rule:

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

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

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

Apply log rule:

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

4 lo g_{5} (\frac{y}{z ^{2}}) = lo g_{5} ((\frac{y}{z ^{2}})^{4})

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

Apply log rule:

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

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

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

Simplify

x^{2} (\frac{y}{z ^{2}})^{4} : \frac{x ^{2} y ^{4}}{z ^{8}}

= lo g_{5} (\frac{x ^{2} y ^{4}}{z ^{8}})

- ln (\frac{C}{V})

ln (2258064 \cdot 1 0^{- 5})

5 lo g_{5} (x) - 25 lo g_{5} (y)

- \frac{5}{4} ln (\frac{1}{4})

ln (- α (x - θ)^{2}) - ln (2 θ^{2} x)

What is 2log_{5}(x)+4(log_{5}(y)-2log_{5}(z)) ?
The solution to 2log_{5}(x)+4(log_{5}(y)-2log_{5}(z)) is log_{5}((x^2y^4)/(z^8))