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Popular >

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

Solution

simplify

2 ln (3 x) - ln (x)

Solution

ln (9 x)

Solution steps

2 ln (3 x) - ln (x)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

\frac{( 3 x ) ^{2}}{x} : 9 x

= ln (9 x)

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Frequently Asked Questions (FAQ)

What is 2ln(3x)-ln(x) ?
The solution to 2ln(3x)-ln(x) is ln(9x)