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Popular >

simplify ln((6^5)/(5^7))

Solution

simplify

ln (\frac{6 ^{5}}{5 ^{7}})

Solution

5 ln (6) - 7 ln (5)

+1

Decimal Notation

- 2.30726 \dots

Solution steps

ln (\frac{6 ^{5}}{5 ^{7}})

Apply log rule:

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

ln (\frac{6 ^{5}}{5 ^{7}}) = ln (6^{5}) - ln (5^{7})

= ln (6^{5}) - ln (5^{7})

Apply log rule:

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

ln (6^{5}) = 5 ln (6)

= 5 ln (6) - ln (5^{7})

Apply log rule:

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

ln (5^{7}) = 7 ln (5)

= 5 ln (6) - 7 ln (5)

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Frequently Asked Questions (FAQ)

What is ln((6^5)/(5^7)) ?
The solution to ln((6^5)/(5^7)) is 5ln(6)-7ln(5)