What is 3log_{a}(y)+3(log_{a}(x)-2log_{a}(z)) ?

The solution to 3log_{a}(y)+3(log_{a}(x)-2log_{a}(z)) is log_{a}((y^3x^3)/(z^6))

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simplify 3log_{a}(y)+3(log_{a}(x)-2log_{a}(z))

simplify

3 lo g_{a} (y) + 3 (lo g_{a} (x) - 2 lo g_{a} (z))

lo g_{a} (\frac{y ^{3} x ^{3}}{z ^{6}})

Solution steps

3 lo g_{a} (y) + 3 (lo g_{a} (x) - 2 lo g_{a} (z))

Apply log rule:

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

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

= 3 lo g_{a} (y) + 3 (lo g_{a} (x) - lo g_{a} (z^{2}))

Apply log rule:

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

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

= 3 lo g_{a} (y) + 3 lo g_{a} (\frac{x}{z ^{2}})

Apply log rule:

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

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

= lo g_{a} (y^{3}) + 3 lo g_{a} (\frac{x}{z ^{2}})

Apply log rule:

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

3 lo g_{a} (\frac{x}{z ^{2}}) = lo g_{a} ((\frac{x}{z ^{2}})^{3})

= lo g_{a} (y^{3}) + lo g_{a} ((\frac{x}{z ^{2}})^{3})

Apply log rule:

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

lo g_{a} (y^{3}) + lo g_{a} ((\frac{x}{z ^{2}})^{3}) = lo g_{a} ((\frac{x}{z ^{2}})^{3} y^{3})

= lo g_{a} ((\frac{x}{z ^{2}})^{3} y^{3})

Simplify

y^{3} (\frac{x}{z ^{2}})^{3} : \frac{y ^{3} x ^{3}}{z ^{6}}

= lo g_{a} (\frac{y ^{3} x ^{3}}{z ^{6}})

ln (2 e^{- 3})

ln (\frac{29}{20})

2000 ln (\frac{140000}{140000 - 2100 ( 8 )}) - 9.8 (8)

ln (x) - ln (t)

\frac{5}{14} lo g_{2} (\frac{5}{14}) + \frac{9}{14} lo g_{2} (\frac{9}{14})

What is 3log_{a}(y)+3(log_{a}(x)-2log_{a}(z)) ?
The solution to 3log_{a}(y)+3(log_{a}(x)-2log_{a}(z)) is log_{a}((y^3x^3)/(z^6))