What is expand log_{4}((m^2n^3)^5) ?

The solution to expand log_{4}((m^2n^3)^5) is 10log_{4}(m)+15log_{4}(n)

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expand log_{4}((m^2n^3)^5)

expand

lo g_{4} ((m^{2} n^{3})^{5})

10 lo g_{4} (m) + 15 lo g_{4} (n)

Solution steps

lo g_{4} ((m^{2} n^{3})^{5})

Apply log rule:

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

lo g_{4} ((m^{2} n^{3})^{5}) = 5 lo g_{4} (m^{2} n^{3})

= 5 lo g_{4} (m^{2} n^{3})

Apply log rule:

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

5 lo g_{4} (m^{2} n^{3}) = 5 lo g_{4} (m^{2}) + 5 lo g_{4} (n^{3})

= 5 lo g_{4} (m^{2}) + 5 lo g_{4} (n^{3})

Apply log rule:

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

lo g_{4} (m^{2}) = 2 lo g_{4} (m)

= 5 \cdot 2 lo g_{4} (m) + 5 lo g_{4} (n^{3})

Apply log rule:

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

lo g_{4} (n^{3}) = 3 lo g_{4} (n)

= 5 \cdot 2 lo g_{4} (m) + 5 \cdot 3 lo g_{4} (n)

Multiply the numbers:

5 \cdot 2 = 10

= 10 lo g_{4} (m) + 5 \cdot 3 lo g_{4} (n)

Multiply the numbers:

5 \cdot 3 = 15

= 10 lo g_{4} (m) + 15 lo g_{4} (n)

ln (\frac{10}{1})

lo g_{10} (\frac{z ^{2} y}{x ^{2}})

lo g_{3} (12 x^{7})

lo g_{10} (4 \cdot 1 0^{- 5})

3 ln (x) - 3 ln (y)

What is expand log_{4}((m^2n^3)^5) ?
The solution to expand log_{4}((m^2n^3)^5) is 10log_{4}(m)+15log_{4}(n)