What is log_{3}(30x(3x+4)) ?

The solution to log_{3}(30x(3x+4)) is 1+log_{3}(10)+log_{3}(x)+log_{3}(3x+4)

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simplify log_{3}(30x(3x+4))

simplify

lo g_{3} (30 x (3 x + 4))

1 + lo g_{3} (10) + lo g_{3} (x) + lo g_{3} (3 x + 4)

Solution steps

lo g_{3} (30 x (3 x + 4))

Factor the number:

30 = 3 \cdot 10

= lo g_{3} (3 \cdot 10 x (3 x + 4))

Apply log rule:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

lo g_{3} (3 \cdot 10 x (3 x + 4)) = lo g_{3} (3) + lo g_{3} (10 x (3 x + 4))

= lo g_{3} (3) + lo g_{3} (10 x (3 x + 4))

Apply log rule:

lo g_{a} (a) = 1

lo g_{3} (3) = 1

= 1 + lo g_{3} (10 x (3 x + 4))

Apply log rule:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

lo g_{3} (10 x (3 x + 4)) = lo g_{3} (10) + lo g_{3} (x) + lo g_{3} (3 x + 4)

= 1 + (lo g_{3} (10) + lo g_{3} (x) + lo g_{3} (3 x + 4))

Apply rule:

a + (b + c) = a + b + c

1 + (lo g_{3} (10) + lo g_{3} (x) + lo g_{3} (3 x + 4)) = 1 + lo g_{3} (10) + lo g_{3} (x) + lo g_{3} (3 x + 4)

= 1 + lo g_{3} (10) + lo g_{3} (x) + lo g_{3} (3 x + 4)

\frac{1}{2} (lo g_{10} (x) + lo g_{10} (y))

ln (y) + ln (x)

3 ln (x) - \frac{1}{9} ln (y)

- \frac{4}{7} lo g_{2} (\frac{4}{7}) - \frac{3}{7} lo g_{2} (\frac{3}{7})

lo g_{b} (x^{3} z)

What is log_{3}(30x(3x+4)) ?
The solution to log_{3}(30x(3x+4)) is 1+log_{3}(10)+log_{3}(x)+log_{3}(3x+4)