What is 2(log_{7}(y)-2log_{7}(w))+3log_{7}(z) ?

The solution to 2(log_{7}(y)-2log_{7}(w))+3log_{7}(z) is log_{7}((y^2z^3)/(w^4))

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simplify 2(log_{7}(y)-2log_{7}(w))+3log_{7}(z)

simplify

2 (lo g_{7} (y) - 2 lo g_{7} (w)) + 3 lo g_{7} (z)

lo g_{7} (\frac{y ^{2} z ^{3}}{w ^{4}})

Solution steps

2 (lo g_{7} (y) - 2 lo g_{7} (w)) + 3 lo g_{7} (z)

Apply log rule:

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

2 lo g_{7} (w) = lo g_{7} (w^{2})

= 2 (lo g_{7} (y) - lo g_{7} (w^{2})) + 3 lo g_{7} (z)

Apply log rule:

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

lo g_{7} (y) - lo g_{7} (w^{2}) = lo g_{7} (\frac{y}{w ^{2}})

= 2 lo g_{7} (\frac{y}{w ^{2}}) + 3 lo g_{7} (z)

Apply log rule:

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

2 lo g_{7} (\frac{y}{w ^{2}}) = lo g_{7} ((\frac{y}{w ^{2}})^{2})

= lo g_{7} ((\frac{y}{w ^{2}})^{2}) + 3 lo g_{7} (z)

Apply log rule:

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

3 lo g_{7} (z) = lo g_{7} (z^{3})

= lo g_{7} ((\frac{y}{w ^{2}})^{2}) + lo g_{7} (z^{3})

Apply log rule:

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

lo g_{7} ((\frac{y}{w ^{2}})^{2}) + lo g_{7} (z^{3}) = lo g_{7} ((\frac{y}{w ^{2}})^{2} z^{3})

= lo g_{7} ((\frac{y}{w ^{2}})^{2} z^{3})

Simplify

(\frac{y}{w ^{2}})^{2} z^{3} : \frac{y ^{2} z ^{3}}{w ^{4}}

= lo g_{7} (\frac{y ^{2} z ^{3}}{w ^{4}})

ln (\frac{10 π - 3 3}{6})

\frac{ln ( 2 ) - ln ( 3 )}{- ln ( 3 )}

- lo g_{10} (5.4 \cdot 1 0^{- 5})

- 8.314 \cdot ln (\frac{10}{1})

lo g_{6} (x + 2) + lo g_{6} (x) - \frac{1}{2} lo g_{6} (x + 1)

What is 2(log_{7}(y)-2log_{7}(w))+3log_{7}(z) ?
The solution to 2(log_{7}(y)-2log_{7}(w))+3log_{7}(z) is log_{7}((y^2z^3)/(w^4))