What is expand log_{10}((x^3y^4)/(z^6)) ?

The solution to expand log_{10}((x^3y^4)/(z^6)) is 3log_{10}(x)+4log_{10}(y)-6log_{10}(z)

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expand log_{10}((x^3y^4)/(z^6))

expand

lo g_{10} (\frac{x ^{3} y ^{4}}{z ^{6}})

3 lo g_{10} (x) + 4 lo g_{10} (y) - 6 lo g_{10} (z)

Solution steps

lo g_{10} (\frac{x ^{3} y ^{4}}{z ^{6}})

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 ^{6}}) = lo g_{10} (x^{3} y^{4}) - lo g_{10} (z^{6})

= lo g_{10} (x^{3} y^{4}) - lo g_{10} (z^{6})

Apply log rule:

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

lo g_{10} (z^{6}) = 6 lo g_{10} (z)

= lo g_{10} (x^{3} y^{4}) - 6 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}) - 6 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}) - 6 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) - 6 lo g_{10} (z)

lo g_{10} (a y^{2})

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

3.3 (lo g_{10} (18000) - lo g_{10} (150))

2 ln (x + 3) + ln (x - 3) - ln (x^{2} - 9)

\frac{1}{2} (lo g_{6} (k^{9}) - lo g_{6} (k^{3}))

What is expand log_{10}((x^3y^4)/(z^6)) ?
The solution to expand log_{10}((x^3y^4)/(z^6)) is 3log_{10}(x)+4log_{10}(y)-6log_{10}(z)