Solve lg(101300/x)=40630/21303*8.314*(-1/373.15+1/367.15)

$$\lg ( \frac { 101300 } { x } ) = \frac { 40630 } { 21303 \times 8.314 } \times ( \frac { - 1 } { 373.15 } + \frac { 1 } { 367.15 } )$$

Evaluate

$$\frac{956000000}{95156308491489}\approx 0.000010047$$

Solution Steps

Multiply 21303 and 8.314 to get 177113.142.

$$\frac{40630}{177113.142}\left(\frac{-1}{373.15}+\frac{1}{367.15}\right)$$

Expand \frac{40630}{177113.142} by multiplying both numerator and the denominator by 1000.

$$\frac{40630000}{177113142}\left(\frac{-1}{373.15}+\frac{1}{367.15}\right)$$

Reduce the fraction \frac{40630000}{177113142} to lowest terms by extracting and canceling out 2.

$$\frac{20315000}{88556571}\left(\frac{-1}{373.15}+\frac{1}{367.15}\right)$$

Expand \frac{-1}{373.15} by multiplying both numerator and the denominator by 100.

$$\frac{20315000}{88556571}\left(\frac{-100}{37315}+\frac{1}{367.15}\right)$$

Reduce the fraction \frac{-100}{37315} to lowest terms by extracting and canceling out 5.

$$\frac{20315000}{88556571}\left(-\frac{20}{7463}+\frac{1}{367.15}\right)$$

Expand \frac{1}{367.15} by multiplying both numerator and the denominator by 100.

$$\frac{20315000}{88556571}\left(-\frac{20}{7463}+\frac{100}{36715}\right)$$

Reduce the fraction \frac{100}{36715} to lowest terms by extracting and canceling out 5.

$$\frac{20315000}{88556571}\left(-\frac{20}{7463}+\frac{20}{7343}\right)$$

Least common multiple of 7463 and 7343 is 54800809. Convert -\frac{20}{7463} and \frac{20}{7343} to fractions with denominator 54800809.

$$\frac{20315000}{88556571}\left(-\frac{146860}{54800809}+\frac{149260}{54800809}\right)$$

Since -\frac{146860}{54800809} and \frac{149260}{54800809} have the same denominator, add them by adding their numerators.

$$\frac{20315000}{88556571}\times \frac{-146860+149260}{54800809}$$

Add -146860 and 149260 to get 2400.

$$\frac{20315000}{88556571}\times \frac{2400}{54800809}$$

Multiply \frac{20315000}{88556571} times \frac{2400}{54800809} by multiplying numerator times numerator and denominator times denominator.

$$\frac{20315000\times 2400}{88556571\times 54800809}$$

Do the multiplications in the fraction \frac{20315000\times 2400}{88556571\times 54800809}.

$$\frac{48756000000}{4852971733065939}$$

Reduce the fraction \frac{48756000000}{4852971733065939} to lowest terms by extracting and canceling out 51.

$$\frac{956000000}{95156308491489}$$

Factor

$$\frac{239 \cdot 2 ^ {8} \cdot 5 ^ {6}}{7 \cdot 263 \cdot 439 \cdot 1049 \cdot 4157 \cdot 3 ^ {3}} = 1.0046627650393845 \times 10^{-5}$$