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Popular >

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

Solution

simplify

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

Solution

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

+1

Decimal Notation

- 7.94182 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

ln (5^{4}) = 4 ln (5)

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

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

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

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Frequently Asked Questions (FAQ)

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