What is 4log_{m}(w)-2log_{m}(z)+3log_{m}(y) ?

The solution to 4log_{m}(w)-2log_{m}(z)+3log_{m}(y) is log_{m}((w^4y^3)/(z^2))

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simplify 4log_{m}(w)-2log_{m}(z)+3log_{m}(y)

simplify

4 lo g_{m} (w) - 2 lo g_{m} (z) + 3 lo g_{m} (y)

lo g_{m} (\frac{w ^{4} y ^{3}}{z ^{2}})

Solution steps

4 lo g_{m} (w) - 2 lo g_{m} (z) + 3 lo g_{m} (y)

Apply log rule:

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

4 lo g_{m} (w) = lo g_{m} (w^{4})

= lo g_{m} (w^{4}) - 2 lo g_{m} (z) + 3 lo g_{m} (y)

Apply log rule:

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

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

= lo g_{m} (w^{4}) - lo g_{m} (z^{2}) + 3 lo g_{m} (y)

Apply log rule:

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

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

= lo g_{m} (\frac{w ^{4}}{z ^{2}}) + 3 lo g_{m} (y)

Apply log rule:

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

3 lo g_{m} (y) = lo g_{m} (y^{3})

= lo g_{m} (\frac{w ^{4}}{z ^{2}}) + lo g_{m} (y^{3})

Apply log rule:

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

lo g_{m} (\frac{w ^{4}}{z ^{2}}) + lo g_{m} (y^{3}) = lo g_{m} (\frac{w ^{4}}{z ^{2}} y^{3})

= lo g_{m} (\frac{w ^{4}}{z ^{2}} y^{3})

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= lo g_{m} (\frac{w ^{4} y ^{3}}{z ^{2}})

\frac{3 \cdot 4 π \cdot 1 0 ^{- 7}}{2 π} ln (\frac{10}{5})

3 lo g_{10} (x) - \frac{1}{2} lo g_{10} (z)

ln (\frac{2 ^{\frac{34}{5}} x ^{15}}{y ^{20}})

ln ((t) (t + 4) (t + 6))

ln (\frac{40}{450})

What is 4log_{m}(w)-2log_{m}(z)+3log_{m}(y) ?
The solution to 4log_{m}(w)-2log_{m}(z)+3log_{m}(y) is log_{m}((w^4y^3)/(z^2))