What is ln((x^3(y-2))/e) ?

The solution to ln((x^3(y-2))/e) is 3ln(x)+ln(y-2)-1

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simplify ln((x^3(y-2))/e)

simplify

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

3 ln (x) + ln (y - 2) - 1

Solution steps

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

Apply log rule:

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

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

= ln (x^{3} (y - 2)) - ln (e)

Apply log rule:

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

ln (x^{3} (y - 2)) = ln (x^{3}) + ln (y - 2)

= ln (x^{3}) + ln (y - 2) - ln (e)

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

= 3 ln (x) + ln (y - 2) - ln (e)

Apply log rule:

lo g_{a} (a) = 1

= 3 ln (x) + ln (y - 2) - 1

ln (6) + ln (\frac{e ^{(2.48344)}}{3})

ln (\frac{1}{2} ln (x^{5} - 2 x))

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

- lo g_{10} (2.8 \cdot 1 0^{- 4})

5 lo g_{10} (x) + 3 lo g_{10} (y)