What is log_{10}(6)+2log_{10}(x)+4log_{10}(y) ?

The solution to log_{10}(6)+2log_{10}(x)+4log_{10}(y) is log_{10}(6x^2y^4)

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simplify log_{10}(6)+2log_{10}(x)+4log_{10}(y)

simplify

lo g_{10} (6) + 2 lo g_{10} (x) + 4 lo g_{10} (y)

lo g_{10} (6 x^{2} y^{4})

Solution steps

lo g_{10} (6) + 2 lo g_{10} (x) + 4 lo g_{10} (y)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

= lo g_{10} (6) + lo g_{10} (x^{2}) + 4 lo g_{10} (y)

Apply log rule:

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

lo g_{10} (6) + lo g_{10} (x^{2}) = lo g_{10} (6 x^{2})

= lo g_{10} (6 x^{2}) + 4 lo g_{10} (y)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

= lo g_{10} (6 x^{2}) + lo g_{10} (y^{4})

Apply log rule:

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

lo g_{10} (6 x^{2}) + lo g_{10} (y^{4}) = lo g_{10} (6 x^{2} y^{4})

= lo g_{10} (6 x^{2} y^{4})

lo g_{6} ((3 \cdot 11)^{6})

\frac{4 ln ( \frac{54}{7} )}{ln ( 2 )}

ln (\frac{1}{3})

π^{81} (ln (11) - 3 ln (2))

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

What is log_{10}(6)+2log_{10}(x)+4log_{10}(y) ?
The solution to log_{10}(6)+2log_{10}(x)+4log_{10}(y) is log_{10}(6x^2y^4)