What is ln((3^n)/(θ^{3n)}) ?

The solution to ln((3^n)/(θ^{3n)}) is nln(3)-3nln(θ)

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simplify ln((3^n)/(θ^{3n)})

simplify

ln (\frac{3 ^{n}}{θ ^{3 n}})

n ln (3) - 3 n ln (θ)

Solution steps

ln (\frac{3 ^{n}}{θ ^{3 n}})

Apply log rule:

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

ln (\frac{3 ^{n}}{θ ^{3 n}}) = ln (3^{n}) - ln (θ^{3 n})

= ln (3^{n}) - ln (θ^{3 n})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

= n ln (3) - ln (θ^{3 n})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (θ^{3 n}) = 3 n ln (θ)

= n ln (3) - 3 n ln (θ)

ln (\frac{1 - sin ( x )}{1 + sin ( x )})

0.0296 (46 e^{(\frac{l n ( 263 ) - l n ( 46 )}{30}) \cdot 2})

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

lo g_{2} (0.05) + lo g_{2} (0.1)

ln (\frac{e ^{- x} x ^{y}}{y !})

What is ln((3^n)/(θ^{3n)}) ?
The solution to ln((3^n)/(θ^{3n)}) is nln(3)-3nln(θ)