What is expand log_{10}(x^2y^4) ?

The solution to expand log_{10}(x^2y^4) is 2log_{10}(x)+4log_{10}(y)

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expand log_{10}(x^2y^4)

expand

lo g_{10} (x^{2} y^{4})

2 lo g_{10} (x) + 4 lo g_{10} (y)

Solution steps

lo g_{10} (x^{2} y^{4})

Apply log rule:

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

lo g_{10} (x^{2} y^{4}) = lo g_{10} (x^{2}) + lo g_{10} (y^{4})

= lo g_{10} (x^{2}) + lo g_{10} (y^{4})

Apply log rule:

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

lo g_{10} (x^{2}) = 2 lo g_{10} (x)

= 2 lo g_{10} (x) + lo g_{10} (y^{4})

Apply log rule:

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

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

= 2 lo g_{10} (x) + 4 lo g_{10} (y)

lo g_{10} (\frac{a ^{3} b ^{2}}{c ^{4}})

lo g_{\frac{1}{2}} (\frac{3}{4})

4 lo g_{10} (3) + lo g_{10} (2)

lo g_{10} (x^{3}) - lo g_{10} (y^{2})

\frac{1}{3} ln (x - 3) - 4 ln (z) + ln (y + 7)

What is expand log_{10}(x^2y^4) ?
The solution to expand log_{10}(x^2y^4) is 2log_{10}(x)+4log_{10}(y)