What is 20ln((1400)/(1400+100(20)))+9.8(20) ?

The solution to 20ln((1400)/(1400+100(20)))+9.8(20) is 20(ln(1400)-ln(3400))+196

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simplify 20ln((1400)/(1400+100(20)))+9.8(20)

simplify

20 ln (\frac{1400}{1400 + 100 ( 20 )}) + 9.8 (20)

20 (ln (1400) - ln (3400)) + 196

Decimal Notation

178.25393 \dots

Solution steps

20 ln (\frac{1400}{1400 + 100 ( 20 )}) + 9.8 (20)

Apply log rule:

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

ln (\frac{1400}{1400 + 100 ( 20 )}) = ln (1400) - ln (1400 + 100 (20))

= 20 (ln (1400) - ln (1400 + 100 \cdot 20)) + 20 \cdot 9.8

ln (1400 + 100 \cdot 20) = ln (3400)

= 20 (ln (1400) - ln (3400)) + 20 \cdot 9.8

Multiply the numbers:

9.8 \cdot 20 = 196

= 20 (ln (1400) - ln (3400)) + 196

- lo g_{10} (1.6 \times 1 0^{- 4})

lo g_{4} (\frac{4}{x})

lo g_{10} (2) + lo g_{10} (12)

\frac{lo g _{10} ( 8 ) 3 + lo g _{10} ( 9 ) 3}{lo g _{10} ( 6 )}

lo g_{10} (\frac{x}{y})

What is 20ln((1400)/(1400+100(20)))+9.8(20) ?
The solution to 20ln((1400)/(1400+100(20)))+9.8(20) is 20(ln(1400)-ln(3400))+196