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Popular >

simplify ln(x)-ln(3x)

Solution

simplify

ln (x) - ln (3 x)

Solution

- ln (3)

+1

Decimal Notation

- 1.09861 \dots

Solution steps

ln (x) - ln (3 x)

Apply log rule:

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

ln (x) - ln (3 x) = ln (\frac{x}{3 x})

= ln (\frac{x}{3 x})

Cancel the common factor:

x

= ln (\frac{1}{3})

Apply log rule:

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

= - ln (3)

Popular Examples

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ln (\frac{1}{1 - 0.97})

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ln (\frac{e ^{8} - 1}{e ^{2} - 1}) - 3

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4 ln (2 x)

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ln (a e^{a (- 5)} (- 5))

limit as x approaches infinity of ln(1/x)

x \to \infty lim (ln (\frac{1}{x}))

Frequently Asked Questions (FAQ)

What is ln(x)-ln(3x) ?
The solution to ln(x)-ln(3x) is -ln(3)