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Popular >

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

Solution

simplify

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

Solution

ln (\frac{4}{27 x})

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

\frac{( 2 x ) ^{2}}{( 3 x ) ^{3}} : \frac{4}{27 x}

= ln (\frac{4}{27 x})

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Frequently Asked Questions (FAQ)

What is 2ln(2x)-3ln(3x) ?
The solution to 2ln(2x)-3ln(3x) is ln(4/(27x))