What is 2log_{a}(7x^3)-1/6 log_{a}(9x+5) ?

The solution to 2log_{a}(7x^3)-1/6 log_{a}(9x+5) is log_{a}((49x^6(9x+5)^{5/6})/(9x+5))

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simplify 2log_{a}(7x^3)-1/6 log_{a}(9x+5)

simplify

2 lo g_{a} (7 x^{3}) - \frac{1}{6} lo g_{a} (9 x + 5)

lo g_{a} (\frac{49 x ^{6} ( 9 x + 5 ) ^{\frac{5}{6}}}{9 x + 5})

Solution steps

2 lo g_{a} (7 x^{3}) - \frac{1}{6} lo g_{a} (9 x + 5)

Apply log rule:

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

2 lo g_{a} (7 x^{3}) = lo g_{a} ((7 x^{3})^{2})

= lo g_{a} ((7 x^{3})^{2}) - \frac{1}{6} lo g_{a} (9 x + 5)

Apply log rule:

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

\frac{1}{6} lo g_{a} (9 x + 5) = lo g_{a} ((9 x + 5)^{\frac{1}{6}})

= lo g_{a} ((7 x^{3})^{2}) - lo g_{a} ((9 x + 5)^{\frac{1}{6}})

Apply log rule:

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

lo g_{a} ((7 x^{3})^{2}) - lo g_{a} ((9 x + 5)^{\frac{1}{6}}) = lo g_{a} (\frac{( 7 x ^{3} ) ^{2}}{( 9 x + 5 ) ^{\frac{1}{6}}})

= lo g_{a} (\frac{( 7 x ^{3} ) ^{2}}{( 9 x + 5 ) ^{\frac{1}{6}}})

Simplify

\frac{( 7 x ^{3} ) ^{2}}{( 9 x + 5 ) ^{\frac{1}{6}}} : \frac{49 x ^{6} ( 9 x + 5 ) ^{\frac{5}{6}}}{9 x + 5}

= lo g_{a} (\frac{49 x ^{6} ( 9 x + 5 ) ^{\frac{5}{6}}}{9 x + 5})

ln (\frac{v ^{2}}{2 α e ^{- β s}})

lo g_{10} (\frac{3 x}{y ^{3}})

\frac{1}{- 0.20698} ln (\frac{28}{118})

\frac{1}{2} ln (\frac{x ^{2} + ( y - 1 ) ^{2}}{x ^{2}}) + ln (x)

2 ln (+ x^{3} ln (x))

What is 2log_{a}(7x^3)-1/6 log_{a}(9x+5) ?
The solution to 2log_{a}(7x^3)-1/6 log_{a}(9x+5) is log_{a}((49x^6(9x+5)^{5/6})/(9x+5))