What is ln(2.8*((12-1.8))/(1.8*(12-2.8))) ?

The solution to ln(2.8*((12-1.8))/(1.8*(12-2.8))) is ln(2.8)++ln(12-1.8)-(ln(1.8)+ln(12-2.8))

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simplify ln(2.8((12-1.8))/(1.8(12-2.8)))

simplify

ln (2.8 \cdot \frac{( 12 - 1.8 )}{1.8 \cdot ( 12 - 2.8 )})

ln (2.8) + + ln (12 - 1.8) - (ln (1.8) + ln (12 - 2.8))

Decimal Notation

0.54501 \dots

Solution steps

ln (2.8 \cdot \frac{( 12 - 1.8 )}{1.8 ( 12 - 2.8 )})

Apply log rule:

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

ln (2.8 \cdot \frac{( 12 - 1.8 )}{1.8 ( 12 - 2.8 )}) = ln (2.8) + ln (\frac{( 12 - 1.8 )}{1.8 ( 12 - 2.8 )})

= ln (2.8) + ln (\frac{( 12 - 1.8 )}{1.8 ( 12 - 2.8 )})

Apply log rule:

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

ln (\frac{( 12 - 1.8 )}{1.8 ( 12 - 2.8 )}) = ln ((12 - 1.8)) - ln (1.8 (12 - 2.8))

= ln (2.8) + + ln (12 - 1.8) - ln (1.8 (12 - 2.8))

Apply log rule:

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

ln (1.8 (12 - 2.8)) = ln (1.8) + ln (12 - 2.8)

= ln (2.8) + + ln (12 - 1.8) - (ln (1.8) + ln (12 - 2.8))

ln (a^{c} b^{g})

- \frac{8.31 \cdot 310}{1 \cdot 9.65 \cdot 1 0 ^{- 4}} \cdot ln (\frac{10}{145})

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

4 lo g_{10} (2) - 3 lo g_{10} (4) + lo g_{10} (5)

ln (3 x^{2} - 9 x) + ln (\frac{1}{3 x})

What is ln(2.8*((12-1.8))/(1.8*(12-2.8))) ?
The solution to ln(2.8*((12-1.8))/(1.8*(12-2.8))) is ln(2.8)++ln(12-1.8)-(ln(1.8)+ln(12-2.8))