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Popular >

simplify ln(x/2)-ln(x)

Solution

simplify

ln (\frac{x}{2}) - ln (x)

Solution

- ln (2)

+1

Decimal Notation

- 0.69314 \dots

Solution steps

ln (\frac{x}{2}) - ln (x)

Apply log rule:

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

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

= ln (\frac{\frac{x}{2}}{x})

\frac{\frac{x}{2}}{x} = \frac{1}{2}

= ln (\frac{1}{2})

Apply log rule:

lo g_{a} (\frac{1}{x}) = - lo g_{a} (x)

= - ln (2)

Popular Examples

simplify 2log_{10}(a)-log_{10}(b)simplify

2 lo g_{10} (a) - lo g_{10} (b)

simplify log_{10}((11x^3)/4)simplify

lo g_{10} (\frac{11 x ^{3}}{4})

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ln (sin (θ)) - ln (\frac{sin ( θ )}{6})

simplify log_{10}(x)-3log_{10}(y)-2log_{10}(z)simplify

lo g_{10} (x) - 3 lo g_{10} (y) - 2 lo g_{10} (z)

simplify 1/3 log_{10}(x)+2log_{10}(y)simplify

\frac{1}{3} lo g_{10} (x) + 2 lo g_{10} (y)

Frequently Asked Questions (FAQ)

What is ln(x/2)-ln(x) ?
The solution to ln(x/2)-ln(x) is -ln(2)