What is ln(8/(3.14^2)*((190-45))/(65-45)) ?

The solution to ln(8/(3.14^2)*((190-45))/(65-45)) is ln(8)-2ln(3.14)++ln(190-45)-ln(65-45)

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simplify ln(8/(3.14^2)*((190-45))/(65-45))

simplify

ln (\frac{8}{3.1 4 ^{2}} \cdot \frac{( 190 - 45 )}{65 - 45})

ln (8) - 2 ln (3.14) + + ln (190 - 45) - ln (65 - 45)

Decimal Notation

1.77199 \dots

Solution steps

ln (\frac{8}{3.1 4 ^{2}} \cdot \frac{( 190 - 45 )}{65 - 45})

Apply log rule:

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

ln (\frac{8}{3.1 4 ^{2}} \cdot \frac{( 190 - 45 )}{65 - 45}) = ln (\frac{8}{3.1 4 ^{2}}) + ln (\frac{( 190 - 45 )}{65 - 45})

= ln (\frac{8}{3.1 4 ^{2}}) + ln (\frac{( 190 - 45 )}{65 - 45})

Apply log rule:

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

ln (\frac{8}{3.1 4 ^{2}}) = ln (8) - ln (3.1 4^{2}), ln (\frac{190 - 45}{65 - 45}) = ln (190 - 45) - ln (65 - 45)

= ln (8) - ln (3.1 4^{2}) + + ln (190 - 45) - ln (65 - 45)

Apply log rule:

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

ln (3.1 4^{2}) = 2 ln (3.14)

= ln (8) - 2 ln (3.14) + + ln (190 - 45) - ln (65 - 45)

25 + 12 ln (x) + 18 ln (y)

3 ln (2) + 2 ln (x) - \frac{1}{2} ln (x + 5)

3 ln (y) - 2 ln (t)

ln (x cos (c) x)

lo g_{1.8} (\frac{3.98}{10.4}) + 55.71 - 54.41

What is ln(8/(3.14^2)*((190-45))/(65-45)) ?
The solution to ln(8/(3.14^2)*((190-45))/(65-45)) is ln(8)-2ln(3.14)++ln(190-45)-ln(65-45)