What is ln(x)e^3-3ln(e/x) ?

The solution to ln(x)e^3-3ln(e/x) is ln((x^{e^3+3})/(e^3))

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simplify ln(x)e^3-3ln(e/x)

simplify

ln (x) e^{3} - 3 ln (\frac{e}{x})

ln (\frac{x ^{e^{3} + 3}}{e ^{3}})

Solution steps

ln (x) e^{3} - 3 ln (\frac{e}{x})

Apply log rule:

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

e^{3} ln (x) = ln (x^{e^{3}})

= ln (x^{e^{3}}) - 3 ln (\frac{e}{x})

Apply log rule:

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

3 ln (\frac{e}{x}) = ln ((\frac{e}{x})^{3})

= ln (x^{e^{3}}) - ln ((\frac{e}{x})^{3})

Apply log rule:

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

ln (x^{e^{3}}) - ln ((\frac{e}{x})^{3}) = ln (\frac{x ^{e^{3}}}{( \frac{e}{x} ) ^{3}})

= ln (\frac{x ^{e^{3}}}{( \frac{e}{x} ) ^{3}})

Simplify

\frac{x ^{e^{3}}}{( \frac{e}{x} ) ^{3}} : \frac{x ^{e^{3} + 3}}{e ^{3}}

= ln (\frac{x ^{e^{3} + 3}}{e ^{3}})

- ln (1 + x) + ln (x)

ln (\frac{c a a}{b})

ln (1 - 1 - x^{2}) - ln (x)

ln (1) - ln (2) - ln (3)

ln (3 \cdot 1 5^{3})

What is ln(x)e^3-3ln(e/x) ?
The solution to ln(x)e^3-3ln(e/x) is ln((x^{e^3+3})/(e^3))