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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

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

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

\frac{ln ( \frac{15}{2} )}{2 ln ( 2 )}

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

ln (\frac{x ^{6} - x}{x ^{3} + 2})

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