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Popular >

simplify 3ln(3a)-ln(9a^3)

Solution

simplify

3 ln (3 a) - ln (9 a^{3})

Solution

ln (3)

+1

Decimal Notation

1.09861 \dots

Solution steps

3 ln (3 a) - ln (9 a^{3})

Apply log rule:

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

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

= ln ((3 a)^{3}) - ln (9 a^{3})

Apply log rule:

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

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

= ln (\frac{( 3 a ) ^{3}}{9 a ^{3}})

\frac{( 3 a ) ^{3}}{9 a ^{3}} = 3

= ln (3)

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Frequently Asked Questions (FAQ)

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