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Popular >

simplify ln((2^5)/(3^7))

Solution

simplify

ln (\frac{2 ^{5}}{3 ^{7}})

Solution

5 ln (2) - 7 ln (3)

+1

Decimal Notation

- 4.22455 \dots

Solution steps

ln (\frac{2 ^{5}}{3 ^{7}})

Apply log rule:

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

ln (\frac{2 ^{5}}{3 ^{7}}) = ln (2^{5}) - ln (3^{7})

= ln (2^{5}) - ln (3^{7})

Apply log rule:

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

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

= 5 ln (2) - ln (3^{7})

Apply log rule:

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

ln (3^{7}) = 7 ln (3)

= 5 ln (2) - 7 ln (3)

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Frequently Asked Questions (FAQ)

What is ln((2^5)/(3^7)) ?
The solution to ln((2^5)/(3^7)) is 5ln(2)-7ln(3)