What is 3log_{e}(x)-4log_{e}(sqrt(y)) ?

The solution to 3log_{e}(x)-4log_{e}(sqrt(y)) is ln((x^3)/(y^2))

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simplify 3log_{e}(x)-4log_{e}(sqrt(y))

simplify

3 lo g_{e} (x) - 4 lo g_{e} (y)

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

Solution steps

3 lo g_{e} (x) - 4 lo g_{e} (y)

Apply log rule:

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

3 lo g_{e} (x) = lo g_{e} (x^{3})

= lo g_{e} (x^{3}) - 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^{3}) - lo g_{e} ((y)^{4})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

lo g_{e} (x^{3}) - lo g_{e} ((y)^{4}) = lo g_{e} (\frac{x ^{3}}{( y ) ^{4}})

= lo g_{e} (\frac{x ^{3}}{( y ) ^{4}})

(y)^{4} = y^{2}

= lo g_{e} (\frac{x ^{3}}{y ^{2}})

Apply log rule:

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

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

lo g_{2} (\frac{16}{y})

- \frac{18 ln ( 2 )}{3 ln ( 2 ) - ln ( 5 )}

ln (\frac{1 + i}{2})

lo g_{\frac{1}{3}} (\frac{x ^{2} - x - 6}{2}) + x + 1

What is 3log_{e}(x)-4log_{e}(sqrt(y)) ?
The solution to 3log_{e}(x)-4log_{e}(sqrt(y)) is ln((x^3)/(y^2))