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Popular >

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

Solution

simplify

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

Solution

2 ln (x) - 3

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

3 ln (e) = 3

= 2 ln (x) - 3

Popular Examples

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\frac{ln ( 60 ) - ln ( 37.8 )}{0.98}

Frequently Asked Questions (FAQ)

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