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Popular >

simplify 4ln(3x)-ln(9x)

Solution

simplify

4 ln (3 x) - ln (9 x)

Solution

ln (9 x^{3})

Solution steps

4 ln (3 x) - ln (9 x)

Apply log rule:

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

4 ln (3 x) = ln ((3 x)^{4})

= ln ((3 x)^{4}) - ln (9 x)

Apply log rule:

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

ln ((3 x)^{4}) - ln (9 x) = ln (\frac{( 3 x ) ^{4}}{9 x})

= ln (\frac{( 3 x ) ^{4}}{9 x})

Simplify

\frac{( 3 x ) ^{4}}{9 x} : 9 x^{3}

= ln (9 x^{3})

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Frequently Asked Questions (FAQ)

What is 4ln(3x)-ln(9x) ?
The solution to 4ln(3x)-ln(9x) is ln(9x^3)