What is ln((3^n)/(2^nb^n)) ?

The solution to ln((3^n)/(2^nb^n)) is ln(3)n-ln(2)n-nln(b)

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simplify ln((3^n)/(2^nb^n))

simplify

ln (\frac{3 ^{n}}{2 ^{n} b ^{n}})

ln (3) n - ln (2) n - n ln (b)

Solution steps

ln (\frac{3 ^{n}}{2 ^{n} b ^{n}})

Apply log rule:

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

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

= ln (3^{n}) - ln (2^{n} b^{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 (2^{n} b^{n})

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (2^{n} b^{n}) = ln (2^{n}) + ln (b^{n})

= ln (3) n - (ln (b^{n}) + ln (2^{n}))

Apply log rule:

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

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

= n ln (3) - (n ln (2) + ln (b^{n}))

Apply log rule:

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

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

= n ln (3) - (n ln (2) + n ln (b))

= ln (3) n - (ln (2) n + n ln (b))

- (n ln (2) + n ln (b)) : - n ln (2) - n ln (b)

= n ln (3) - n ln (2) - n ln (b)

= ln (3) n - ln (2) n - n ln (b)

\frac{6}{5} ln ∣ z - 1 ∣ - \frac{1}{5} ln ∣ z + 4 ∣ + ln ∣ x ∣

ln (2) + \frac{1}{2} ln (5)

2000 ln (\frac{140000}{140000 - 4200}) - (9.8 \cdot 2)

lo g_{b} (\frac{a ^{\frac{- 3}{2}}}{b ^{4}})

ln (a^{5})

What is ln((3^n)/(2^nb^n)) ?
The solution to ln((3^n)/(2^nb^n)) is ln(3)n-ln(2)n-nln(b)