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Popular >

simplify log_{e}(x/e)

Solution

simplify

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

Solution

ln (x) - 1

Solution steps

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

Apply log rule:

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

lo g_{e} (\frac{x}{e}) = lo g_{e} (x) - lo g_{e} (e)

= lo g_{e} (x) - lo g_{e} (e)

Apply log rule:

lo g_{e} (x) = ln (x)

= ln (x) - lo g_{e} (e)

Apply log rule:

lo g_{a} (a) = 1

= ln (x) - 1

Popular Examples

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ln x^{2} + 4 - 2 ln (2)

simplify 1/2 ln(y/x)simplify

\frac{1}{2} ln (\frac{y}{x})

expand log_{3}((x^2)/y)expand

lo g_{3} (\frac{x ^{2}}{y})

simplify x-1/2 log_{15}(17)+1/2 log_{15}(3)simplify

x - \frac{1}{2} lo g_{15} (17) + \frac{1}{2} lo g_{15} (3)

expand log_{9}((x(x^2+7))/(sqrt(x^2-7)))expand

lo g_{9} (\frac{x ( x ^{2} + 7 )}{x ^{2} - 7})

Frequently Asked Questions (FAQ)

What is log_{e}(x/e) ?
The solution to log_{e}(x/e) is ln(x)-1