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Popular >

simplify ln(3x)-2ln(x)

Solution

simplify

ln (3 x) - 2 ln (x)

Solution

ln (\frac{3}{x})

Solution steps

ln (3 x) - 2 ln (x)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

= ln (3 x) - ln (x^{2})

Apply log rule:

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

ln (3 x) - ln (x^{2}) = ln (\frac{3 x}{x ^{2}})

= ln (\frac{3 x}{x ^{2}})

Cancel the common factor:

x

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

Popular Examples

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Frequently Asked Questions (FAQ)

What is ln(3x)-2ln(x) ?
The solution to ln(3x)-2ln(x) is ln(3/x)