What is 6log_{3}(5x+2)+5log_{3}(3x+6) ?

The solution to 6log_{3}(5x+2)+5log_{3}(3x+6) is log_{3}((5x+2)^6(3x+6)^5)

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simplify 6log_{3}(5x+2)+5log_{3}(3x+6)

simplify

6 lo g_{3} (5 x + 2) + 5 lo g_{3} (3 x + 6)

lo g_{3} ((5 x + 2)^{6} (3 x + 6)^{5})

Solution steps

6 lo g_{3} (5 x + 2) + 5 lo g_{3} (3 x + 6)

Apply log rule:

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

6 lo g_{3} (5 x + 2) = lo g_{3} ((5 x + 2)^{6})

= lo g_{3} ((5 x + 2)^{6}) + 5 lo g_{3} (3 x + 6)

Apply log rule:

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

5 lo g_{3} (3 x + 6) = lo g_{3} ((3 x + 6)^{5})

= lo g_{3} ((5 x + 2)^{6}) + lo g_{3} ((3 x + 6)^{5})

Apply log rule:

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

lo g_{3} ((5 x + 2)^{6}) + lo g_{3} ((3 x + 6)^{5}) = lo g_{3} ((5 x + 2)^{6} (3 x + 6)^{5})

= lo g_{3} ((5 x + 2)^{6} (3 x + 6)^{5})

e^{(x - 2 y)} - ln (2 x^{(2)} y)

lo g_{a} (\frac{( 5 ^{2} y )}{- 1 ^{3}})

ln (\frac{1}{0.975})

ln (\frac{0.23113}{4.98 \cdot 1 0 ^{- 3}})

x (ln (3 x - 1) - ln (3 x - 3))

What is 6log_{3}(5x+2)+5log_{3}(3x+6) ?
The solution to 6log_{3}(5x+2)+5log_{3}(3x+6) is log_{3}((5x+2)^6(3x+6)^5)