What is simplify-2000ln(10)+2000ln(20) ?

The solution to simplify-2000ln(10)+2000ln(20) is 8000000000ln(2)

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simplify-2000ln(10)+2000ln(20)

simplify

- 2000 ln (10) + 2000 ln (20)

8000000000 ln (2)

Decimal Notation

5545177444.479563

Solution steps

- 2000 ln (10) + 2000 ln (20)

Apply log rule:

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

ln (20) - ln (10) = ln (\frac{20}{10})

= 2000 \cdot 2000 ln (\frac{20}{10})

\frac{2 0 ^{2000}}{1 0 ^{2000}} = 2^{2000}

= 2000 ln (2^{2000}) \cdot 2000

Simplify

ln (2^{2000}) : 2000 ln (2)

= 2000 \cdot 2000 \cdot 2000 ln (2)

Multiply the numbers:

2000 \cdot 2000 \cdot 2000 = 8000000000

= 8000000000 ln (2)

\frac{1}{4} ln (y - 2) - \frac{1}{4} ln (y + 2)

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What is simplify-2000ln(10)+2000ln(20) ?
The solution to simplify-2000ln(10)+2000ln(20) is 8000000000ln(2)