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Popular >

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

Solution

simplify

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

Solution

ln (x - 3) - x

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

x ln (e) = x

= ln (x - 3) - x

Popular Examples

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ln (9) + \frac{1}{2} ln (x + 4) - 5 ln (1 + x)

simplify log_{10}(x+5)-log_{10}(x^2+9x+20)simplify

lo g_{10} (x + 5) - lo g_{10} (x^{2} + 9 x + 20)

simplify ln(x^{0.1}*0.7)simplify

ln (x^{0.1} \cdot 0.7)

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lo g_{b} (19 x \cdot 18 y)

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lo g_{10} (6) + lo g_{10} (8)

Frequently Asked Questions (FAQ)

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