What is 2ln(3^4)+ln(3^3)-ln(9) ?

The solution to 2ln(3^4)+ln(3^3)-ln(9) is 9ln(3)

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simplify 2ln(3^4)+ln(3^3)-ln(9)

simplify

2 ln (3^{4}) + ln (3^{3}) - ln (9)

9 ln (3)

Decimal Notation

9.88751 \dots

Solution steps

2 ln (3^{4}) + ln (3^{3}) - ln (9)

Apply log rule:

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

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

= 2 ln (3^{4}) + ln (\frac{3 ^{3}}{9})

\frac{3 ^{3}}{9} = 3

= 2 ln (3^{4}) + ln (3)

2 ln (3^{4}) = 8 ln (3)

= 8 ln (3) + ln (3)

Add similar elements:

8 ln (3) + ln (3) = 9 ln (3)

= 9 ln (3)

lo g_{10} ((1 - p)^{x} \cdot p)

ln (\frac{1 + x}{y})

4.76 + lo g_{10} (\frac{11}{4.8})

ln (x^{2} y)

- lo g_{10} (3646974099 x 1 0^{- 3})

What is 2ln(3^4)+ln(3^3)-ln(9) ?
The solution to 2ln(3^4)+ln(3^3)-ln(9) is 9ln(3)