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Popular >

simplify ln((sin(x))/(e^x))

Solution

simplify

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

Solution

ln (sin (x)) - x

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

= ln (sin (x)) - x ln (e)

x ln (e) = x

= ln (sin (x)) - x

Popular Examples

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\frac{\frac{3}{4} ln b ^{3} + 1 - ln ∣ 3 b + 1 ∣}{3}

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ln (\frac{27 - 10}{9.9 - 100})

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3.41 + lo g_{10} (\frac{0.00225}{2.25 \cdot 1 0 ^{- 1}})

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ln (\frac{3 ^{2} + 1}{2 ( 3 ) ^{2} + 1})

Frequently Asked Questions (FAQ)

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