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

The solution to 6log_{e}(x)+4log_{e}(y) is ln(x^6y^4)

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simplify 6log_{e}(x)+4log_{e}(y)

simplify

6 lo g_{e} (x) + 4 lo g_{e} (y)

ln (x^{6} y^{4})

Solution steps

6 lo g_{e} (x) + 4 lo g_{e} (y)

Apply log rule:

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

6 lo g_{e} (x) = lo g_{e} (x^{6})

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{e} (x) = ln (x)

= ln (x^{6} y^{4})

ln (5 x)

- lo g_{0.5} (2 x) - 3

ln (\frac{e ^{(x + 2)} ( 5 x + 1 ) ^{3}}{x ^{5} ( 2 x + 1 ) ^{7}})

\frac{19.16}{0.004 \cdot 0.02} ln (\frac{1}{1 - 0.9})

ln (\frac{e ^{3} y ^{2}}{x})

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