What is simplify-2000ln(0.05-0.0005x)+ln(x) ?

The solution to simplify-2000ln(0.05-0.0005x)+ln(x) is ln(x/((0.05-0.0005x)^{2000)})

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simplify-2000ln(0.05-0.0005x)+ln(x)

simplify

- 2000 ln (0.05 - 0.0005 x) + ln (x)

ln (\frac{x}{( 0.05 - 0.0005 x ) ^{2000}})

Solution steps

- 2000 ln (0.05 - 0.0005 x) + ln (x)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

2000 ln (- 0.0005 x + 0.05) = ln ((- 0.0005 x + 0.05)^{2000})

= - ln ((- 0.0005 x + 0.05)^{2000}) + ln (x)

Apply log rule:

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

ln (x) - ln ((0.05 - 0.0005 x)^{2000}) = ln (\frac{x}{( - 0.0005 x + 0.05 ) ^{2000}})

= ln (\frac{x}{( 0.05 - 0.0005 x ) ^{2000}})

ln (x^{2} (4 - x))

- lo g_{10} (9.6 \cdot 1 0^{- 9})

ln (e^{3 x} \cdot \frac{1}{3})

- lo g_{10} (6.31 x 1 0^{- 11})

lo g_{4} (6 (7^{2})^{3})

What is simplify-2000ln(0.05-0.0005x)+ln(x) ?
The solution to simplify-2000ln(0.05-0.0005x)+ln(x) is ln(x/((0.05-0.0005x)^{2000)})