What is ln((2^2)/(3^35^4)) ?

The solution to ln((2^2)/(3^35^4)) is 2ln(2)-3ln(3)-4ln(5)

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simplify ln((2^2)/(3^35^4))

simplify

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

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

Decimal Notation

- 8.34729 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

= 2 ln (2) - (3 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)

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

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

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

ln (\frac{x x - 9}{x ^{5} + 9})

8 ln (x) - 3 ln (y)

4 lo g_{10} (3 x^{3}) - 12 lo g_{10} (9 x^{8})

ln (9 x^{9}) + ln (10 x^{3})

What is ln((2^2)/(3^35^4)) ?
The solution to ln((2^2)/(3^35^4)) is 2ln(2)-3ln(3)-4ln(5)