What is 2log_{a}(w)-1/2 log_{a}(z)+4log_{a}(y) ?

The solution to 2log_{a}(w)-1/2 log_{a}(z)+4log_{a}(y) is log_{a}((w^2y^4sqrt(z))/z)

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simplify 2log_{a}(w)-1/2 log_{a}(z)+4log_{a}(y)

simplify

2 lo g_{a} (w) - \frac{1}{2} lo g_{a} (z) + 4 lo g_{a} (y)

lo g_{a} (\frac{w ^{2} y ^{4} z}{z})

Solution steps

2 lo g_{a} (w) - \frac{1}{2} lo g_{a} (z) + 4 lo g_{a} (y)

Apply log rule:

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

2 lo g_{a} (w) = lo g_{a} (w^{2})

= lo g_{a} (w^{2}) - \frac{1}{2} lo g_{a} (z) + 4 lo g_{a} (y)

Apply log rule:

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

\frac{1}{2} lo g_{a} (z) = lo g_{a} (z^{\frac{1}{2}})

= lo g_{a} (w^{2}) - lo g_{a} (z^{\frac{1}{2}}) + 4 lo g_{a} (y)

Apply log rule:

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

lo g_{a} (w^{2}) - lo g_{a} (z^{\frac{1}{2}}) = lo g_{a} (\frac{w ^{2}}{z ^{\frac{1}{2}}})

= lo g_{a} (\frac{w ^{2}}{z ^{\frac{1}{2}}}) + 4 lo g_{a} (y)

Simplify

\frac{w ^{2}}{z ^{\frac{1}{2}}} : \frac{w ^{2} z}{z}

= lo g_{a} (\frac{w ^{2} z}{z}) + 4 lo g_{a} (y)

Apply log rule:

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

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

= lo g_{a} (\frac{w ^{2} z}{z}) + lo g_{a} (y^{4})

Apply log rule:

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

lo g_{a} (\frac{w ^{2} z}{z}) + lo g_{a} (y^{4}) = lo g_{a} (\frac{w ^{2} z}{z} y^{4})

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

Simplify

\frac{w ^{2} z}{z} y^{4} : \frac{w ^{2} y ^{4} z}{z}

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

ln (\frac{s ^{2} + 49}{s ^{2} + 25})

ln (y \frac{y}{7 - y})

\frac{1}{4 ( 1 + x ^{4} )} + ln (x) - \frac{1}{4} ln (1 + x^{4})

- lo g_{10} (3.16 \cdot 1 0^{- 8})

What is 2log_{a}(w)-1/2 log_{a}(z)+4log_{a}(y) ?
The solution to 2log_{a}(w)-1/2 log_{a}(z)+4log_{a}(y) is log_{a}((w^2y^4sqrt(z))/z)