What is 1000ln(1/5 |20+sqrt(25+20^2)|) ?

The solution to 1000ln(1/5 |20+sqrt(25+20^2)|) is -1000ln(5)+1000ln(20+5sqrt(17))

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simplify 1000ln(1/5 |20+sqrt(25+20^2)|)

simplify

1000 ln (\frac{1}{5} 20 + 25 + 2 0^{2})

- 1000 ln (5) + 1000 ln (20 + 517)

Decimal Notation

2094.71254 \dots

Solution steps

1000 ln (\frac{1}{5} 20 + 25 + 2 0^{2})

Apply log rule:

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

1000 ln (\frac{1}{5} 20 + 25 + 2 0^{2}) = 1000 ln (\frac{1}{5}) + 1000 ln 20 + 25 + 2 0^{2}

= 1000 ln (\frac{1}{5}) + 1000 ln 2 0^{2} + 25 + 20

Apply log rule:

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

ln (\frac{1}{5}) = ln (1) - ln (5)

= 1000 (ln (1) - ln (5)) + 1000 ln 2 0^{2} + 25 + 20

1000 (ln (1) - ln (5)) = - 1000 ln (5)

= - 1000 ln (5) + 1000 ln 2 0^{2} + 25 + 20

1000 ln 20 + 25 + 2 0^{2} = 1000 ln (20 + 517)

= - 1000 ln (5) + 1000 ln (20 + 517)

3 lo g_{5} (x + 1) - \frac{1}{2} lo g_{5} (w) + 3

- \frac{1}{70} ln (\frac{4.3 ( 2.3 )}{6.7 ( 8.7 )})

\frac{1}{2} lo g_{10} (x) - 4 lo g_{10} (y)

\frac{- 2 ln ( 5 )}{ln ( 5 ) - 2 ln ( 2 )}

ln (a e^{- a (x - b)})

What is 1000ln(1/5 |20+sqrt(25+20^2)|) ?
The solution to 1000ln(1/5 |20+sqrt(25+20^2)|) is -1000ln(5)+1000ln(20+5sqrt(17))