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Popular >

simplify ln(x)-ln(2x)

Solution

simplify

ln (x) - ln (2 x)

Solution

- ln (2)

+1

Decimal Notation

- 0.69314 \dots

Solution steps

ln (x) - ln (2 x)

Apply log rule:

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

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

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

Cancel the common factor:

x

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

Apply log rule:

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

= - ln (2)

Popular Examples

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lo g_{e} (\frac{2}{3})

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ln (\frac{e ^{5}}{12})

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lo g_{10} (20) + lo g_{10} (30)

simplify 1/2 [1+log_{2}(a)-log_{2}(b)-log_{2}(3)]simplify

\frac{1}{2} [1 + lo g_{2} (a) - lo g_{2} (b) - lo g_{2} (3)]

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

Frequently Asked Questions (FAQ)

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