What is expand log_{10}((uv^5)^3) ?

The solution to expand log_{10}((uv^5)^3) is 3log_{10}(u)+15log_{10}(v)

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expand log_{10}((uv^5)^3)

expand

lo g_{10} ((u v^{5})^{3})

3 lo g_{10} (u) + 15 lo g_{10} (v)

Solution steps

lo g_{10} ((u v^{5})^{3})

Apply log rule:

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

lo g_{10} ((u v^{5})^{3}) = 3 lo g_{10} (u v^{5})

= 3 lo g_{10} (u v^{5})

Apply log rule:

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

3 lo g_{10} (u v^{5}) = 3 lo g_{10} (u) + 3 lo g_{10} (v^{5})

= 3 lo g_{10} (u) + 3 lo g_{10} (v^{5})

Apply log rule:

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

lo g_{10} (v^{5}) = 5 lo g_{10} (v)

= 3 lo g_{10} (u) + 3 \cdot 5 lo g_{10} (v)

Multiply the numbers:

3 \cdot 5 = 15

= 3 lo g_{10} (u) + 15 lo g_{10} (v)

- ln (\frac{0.8 - \frac{3}{5}}{1 - \frac{3}{5}})

ln (\frac{30000}{25000})

\frac{3 ln ( 5 ) - 3 ln ( 7 )}{2 ln ( 7 ) - ln ( 5 )}

ln (\frac{2 i + 1}{- 1})

\frac{5 ln ( 3 )}{ln ( \frac{2}{3} )}

What is expand log_{10}((uv^5)^3) ?
The solution to expand log_{10}((uv^5)^3) is 3log_{10}(u)+15log_{10}(v)