What is expand log_{10}((x^3y^4)/(z^3)) ?

The solution to expand log_{10}((x^3y^4)/(z^3)) is 3log_{10}(x)+4log_{10}(y)-3log_{10}(z)

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expand log_{10}((x^3y^4)/(z^3))

expand

lo g_{10} (\frac{x ^{3} y ^{4}}{z ^{3}})

3 lo g_{10} (x) + 4 lo g_{10} (y) - 3 lo g_{10} (z)

Solution steps

lo g_{10} (\frac{x ^{3} y ^{4}}{z ^{3}})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

lo g_{10} (\frac{x ^{3} y ^{4}}{z ^{3}}) = lo g_{10} (x^{3} y^{4}) - lo g_{10} (z^{3})

= lo g_{10} (x^{3} y^{4}) - lo g_{10} (z^{3})

Apply log rule:

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

lo g_{10} (z^{3}) = 3 lo g_{10} (z)

= lo g_{10} (x^{3} y^{4}) - 3 lo g_{10} (z)

Apply log rule:

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

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

= lo g_{10} (x^{3}) + lo g_{10} (y^{4}) - 3 lo g_{10} (z)

Apply log rule:

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

lo g_{10} (x^{3}) = 3 lo g_{10} (x)

= 3 lo g_{10} (x) + lo g_{10} (y^{4}) - 3 lo g_{10} (z)

Apply log rule:

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

lo g_{10} (y^{4}) = 4 lo g_{10} (y)

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

\frac{1}{3} (ln (x) + ln (x - 6) - ln (x^{3} + 9))

\frac{1}{2} lo g_{10} (x + 3) + \frac{1}{2} lo g_{10} (2 x - 1)

\frac{ln ( \frac{69}{97} )}{2 ln ( 2 )}

\frac{1}{5} lo g_{3} (10)

- \frac{1}{16} lo g_{e} (\frac{1}{16}) - \frac{15}{16} lo g_{e} (\frac{15}{16})

What is expand log_{10}((x^3y^4)/(z^3)) ?
The solution to expand log_{10}((x^3y^4)/(z^3)) is 3log_{10}(x)+4log_{10}(y)-3log_{10}(z)