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Popular >

simplify ln(x/(e^{3x)})

Solution

simplify

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

Solution

ln (x) - 3 x

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

3 x ln (e) = 3 x

= ln (x) - 3 x

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Frequently Asked Questions (FAQ)

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