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Popular >

simplify ln(4/(3^{-2)*5})

Solution

simplify

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

Solution

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

+1

Decimal Notation

1.97408 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

ln (4) = 2 ln (2)

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

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

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

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Frequently Asked Questions (FAQ)

What is ln(4/(3^{-2)*5}) ?
The solution to ln(4/(3^{-2)*5}) is 2ln(2)+2ln(3)-ln(5)