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

The solution to 4(log_{a}(w)-4log_{a}(z))+2log_{a}(y) is log_{a}((w^4y^2)/(z^{16)})

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

simplify

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

lo g_{a} (\frac{w ^{4} y ^{2}}{z ^{16}})

Solution steps

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

Apply log rule:

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

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

(\frac{w}{z ^{4}})^{4} y^{2} : \frac{w ^{4} y ^{2}}{z ^{16}}

= lo g_{a} (\frac{w ^{4} y ^{2}}{z ^{16}})

3 ln_{7} (4) + ln_{7} (6)

lo g_{1.8} (\frac{8.13}{3.12}) + 52.11 - 54.01

lo g_{10} (4 p^{3})

- lo g_{10} (5.34 \cdot 1 0^{- 3})

6 [ln (x) - ln (x + 5) - ln (\cdot (- 5))]

What is 4(log_{a}(w)-4log_{a}(z))+2log_{a}(y) ?
The solution to 4(log_{a}(w)-4log_{a}(z))+2log_{a}(y) is log_{a}((w^4y^2)/(z^{16)})