What is ln((2^3)/(3^45^2)) ?

The solution to ln((2^3)/(3^45^2)) is 3ln(2)-4ln(3)-2ln(5)

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simplify ln((2^3)/(3^45^2))

simplify

ln (\frac{2 ^{3}}{3 ^{4} 5 ^{2}})

3 ln (2) - 4 ln (3) - 2 ln (5)

Decimal Notation

- 5.53388 \dots

Solution steps

ln (\frac{2 ^{3}}{3 ^{4} \cdot 5 ^{2}})

Apply log rule:

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

ln (\frac{2 ^{3}}{3 ^{4} \cdot 5 ^{2}}) = ln (2^{3}) - ln (3^{4} \cdot 5^{2})

= ln (2^{3}) - ln (3^{4} \cdot 5^{2})

Apply log rule:

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

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

= 3 ln (2) - ln (3^{4} \cdot 5^{2})

Apply log rule:

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

ln (3^{4} \cdot 5^{2}) = ln (3^{4}) + ln (5^{2})

= 3 ln (2) - (ln (3^{4}) + ln (5^{2}))

Apply log rule:

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

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

= 3 ln (2) - (4 ln (3) + ln (5^{2}))

Apply log rule:

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

ln (5^{2}) = 2 ln (5)

= 3 ln (2) - (4 ln (3) + 2 ln (5))

- (4 ln (3) + 2 ln (5)) : - 4 ln (3) - 2 ln (5)

= 3 ln (2) - 4 ln (3) - 2 ln (5)

lo g_{b} (x) + 2 lo g_{b} (y) - 3 lo g_{b} (z)

lo g_{5} ((x - 1)^{2}) (4 x)

lo g_{10} (\frac{s}{t})

ln (\frac{4 w}{7})

ln (x) + ln (1 - x)

What is ln((2^3)/(3^45^2)) ?
The solution to ln((2^3)/(3^45^2)) is 3ln(2)-4ln(3)-2ln(5)