What is 600ln(600)+400ln(400) ?

The solution to 600ln(600)+400ln(400) is 48000000ln(3.456E13)

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simplify 600ln(600)+400ln(400)

simplify

600 ln (600) + 400 ln (400)

48000000 ln (3.456 E 13)

Decimal Notation

1496338466.87349 \dots

Solution steps

600 ln (600) + 400 ln (400)

Apply log rule:

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

ln (600) + ln (400) = ln (600 \cdot 400)

= 600 \cdot 400 ln (600 \cdot 400)

60 0^{600} \cdot 40 0^{400} = 2^{3400} \cdot 5^{2000} \cdot 3^{600}

= 600 ln (2^{3400} \cdot 5^{2000} \cdot 3^{600}) \cdot 400

Multiply the numbers:

600 \cdot 400 = 240000

= 240000 ln (2^{3400} \cdot 5^{2000} \cdot 3^{600})

Simplify

ln (2^{3400} \cdot 5^{2000} \cdot 3^{600}) : 200 ln (2^{17} \cdot 5^{10} \cdot 3^{3})

= 240000 \cdot 200 ln (2^{17} \cdot 5^{10} \cdot 3^{3})

Multiply the numbers:

240000 \cdot 200 = 48000000

= 48000000 ln (2^{17} \cdot 5^{10} \cdot 3^{3})

2^{17} = 131072

= 48000000 ln (5^{10} \cdot 3^{3} \cdot 131072)

5^{10} = 9765625

= 48000000 ln (3^{3} \cdot 131072 \cdot 9765625)

3^{3} = 27

= 48000000 ln (131072 \cdot 9765625 \cdot 27)

Multiply the numbers:

131072 \cdot 9765625 \cdot 27 = 3.456 E 13

= 48000000 ln (3.456 E 13)

ln (\frac{sin ( y )}{cos ( x )})

ln (x \cdot e^{r})

2 - 4 \cdot (lo g_{e} (25) - lo g_{e} (13))

ln (x) - ln (v) + ln (v^{2} + 12)

\frac{43 π}{10} + ln (7) - \frac{1}{2} \cdot ln (26) - 169760

What is 600ln(600)+400ln(400) ?
The solution to 600ln(600)+400ln(400) is 48000000ln(3.456E13)