What is log_{3}(3(5x)) ?

The solution to log_{3}(3(5x)) is 1+log_{3}(5)+log_{3}(x)

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simplify log_{3}(3(5x))

simplify

lo g_{3} (3 (5 x))

1 + lo g_{3} (5) + lo g_{3} (x)

Solution steps

lo g_{3} (3 (5 x))

Apply log rule:

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

lo g_{3} (3 \cdot 5 x) = lo g_{3} (3) + lo g_{3} (5 x)

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

Apply log rule:

lo g_{a} (a) = 1

lo g_{3} (3) = 1

= 1 + lo g_{3} (5 x)

Apply log rule:

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

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

= 1 + (lo g_{3} (5) + lo g_{3} (x))

Apply rule:

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

1 + (lo g_{3} (5) + lo g_{3} (x)) = 1 + lo g_{3} (5) + lo g_{3} (x)

= 1 + lo g_{3} (5) + lo g_{3} (x)

2 lo g_{10} (5) + 3 lo g_{10} (2)

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

- \frac{2}{7} lo g_{2} (\frac{2}{7}) - \frac{5}{7} lo g_{2} (\frac{5}{7})

lo g_{10} (1.86 \cdot 1 0^{6}) - lo g_{10} (6.9 \cdot 1 0^{4})

6.1 + lo g_{10} (\frac{24.6}{0.0308})

What is log_{3}(3(5x)) ?
The solution to log_{3}(3(5x)) is 1+log_{3}(5)+log_{3}(x)