What is ln((e^{9/2}2(x))/(x^3))-ln((y-2)^3h(x)) ?

The solution to ln((e^{9/2}2(x))/(x^3))-ln((y-2)^3h(x)) is ln((2e^{9/2})/(x^3h(y-2)^3))

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simplify ln((e^{9/2}2(x))/(x^3))-ln((y-2)^3h(x))

simplify

ln (\frac{e ^{\frac{9}{2}} 2 ( x )}{x ^{3}}) - ln ((y - 2)^{3} h (x))

ln (\frac{2 e ^{\frac{9}{2}}}{x ^{3} h ( y - 2 ) ^{3}})

Solution steps

ln (\frac{e ^{\frac{9}{2}} \cdot 2 ( x )}{x ^{3}}) - ln ((y - 2)^{3} h (x))

Apply log rule:

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

ln (\frac{2 e ^{\frac{9}{2}} ( x )}{x ^{3}}) - ln ((x) h (y - 2)^{3}) = ln \frac{\frac{2 e ^{\frac{9}{2}} x}{x ^{3}}}{x h ( y - 2 ) ^{3}}

= ln \frac{\frac{e ^{\frac{9}{2}} \cdot 2 x}{x ^{3}}}{( y - 2 ) ^{3} h x}

Simplify

\frac{\frac{e ^{\frac{9}{2}} \cdot 2 ( x )}{x ^{3}}}{( y - 2 ) ^{3} h ( x )} : \frac{2 e ^{\frac{9}{2}}}{x ^{3} h ( y - 2 ) ^{3}}

= ln (\frac{2 e ^{\frac{9}{2}}}{x ^{3} h ( y - 2 ) ^{3}})

\frac{1}{2} (lo g_{8} (s) + lo g_{8} (t))

lo g_{8} (x (x - 9))

lo g_{10} (x (x^{2} + 2)^{- \frac{1}{2}})

ln (\frac{x}{x})

ln (\frac{2}{7 x ^{7} y})

What is ln((e^{9/2}2(x))/(x^3))-ln((y-2)^3h(x)) ?
The solution to ln((e^{9/2}2(x))/(x^3))-ln((y-2)^3h(x)) is ln((2e^{9/2})/(x^3h(y-2)^3))