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Popular >

simplify ln(x/(e^{2x)})

Solution

simplify

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

Solution

ln (x) - 2 x

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

2 x ln (e) = 2 x

= ln (x) - 2 x

Popular Examples

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lo g_{5} (\frac{5}{x})

simplify log_{10}(4x)+2*log_{10}(x-3)simplify

lo g_{10} (4 x) + 2 \cdot lo g_{10} (x - 3)

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

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(lo g_{2} (x) - lo g_{2} (y)) + 6 lo g_{2} (z)

expand log_{3}((7g^9h^5)^2)expand

lo g_{3} ((7 g^{9} h^{5})^{2})

Frequently Asked Questions (FAQ)

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