What is ln((ex^2)/y) ?

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

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simplify ln((ex^2)/y)

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

ln (e x^{2}) = ln (e) + ln (x^{2})

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

Apply log rule:

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

ln (x^{2}) = 2 ln (x)

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

Apply log rule:

lo g_{a} (a) = 1

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

lo g_{\frac{1}{3}} (\frac{3 x ^{2} - 14 x - 24}{6}) - x + 3

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

3 lo g_{3} (x) + lo g_{3} (4) - 3 lo g_{3} (x - 2)

- \frac{4}{6} lo g_{2} (\frac{4}{6}) - \frac{2}{6} lo g_{2} (\frac{2}{6})

lo g_{5} (6) + lo g_{5} (11)