What is ln((2^4)/(3^25^3)) ?

The solution to ln((2^4)/(3^25^3)) is 4ln(2)-2ln(3)-3ln(5)

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simplify ln((2^4)/(3^25^3))

simplify

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

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

Decimal Notation

- 4.25294 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

ln (5^{3}) = 3 ln (5)

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

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

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

lo g_{2} (13 x + 14) - lo g_{2} (\frac{1}{13 x - 14})

ln (8 z)

lo g_{8} (7 a)

ln (5 e^{6 x})

\frac{2 ln ( 2 )}{2}

What is ln((2^4)/(3^25^3)) ?
The solution to ln((2^4)/(3^25^3)) is 4ln(2)-2ln(3)-3ln(5)