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

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

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expand log_{3}((5x)^3)

expand

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

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

Solution steps

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

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

= 3 lo g_{3} (5 x)

Apply log rule:

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

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

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

ln (\frac{5 + 0.5}{5})

ln (\frac{29000}{21000})

4 ln (x) - 7 ln (y) - ln (z)

ln (5 x) - ln (5 y)

ln (\frac{9}{91})

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