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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

3 ln (e) = 3

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

0.4 lo g_{2} (0.4) + 0.6 lo g_{2} (0.6)

4 \cdot ln (\frac{1}{2})

\frac{1}{2} ln (tan (\frac{x}{2}))

ln (\frac{- a}{2 b - a}) - ln (- 1)

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