ln與log的數學計算..?

1)
In(1000/600) = k
In(5/3) = k
In5 - In3 = k
In(10/2) - In3 = k
In10 - In2 - In3 = k
In10 - In2 - In(10^log3) = k
In10 - In2 - log3 * In10 = k
In10 - In2 - log3 * 2.303 = k
2.303 - 0.693 - 0.477 * 2.303 = k
k = 0.5115

代入2)
In(600/A) = 0.5115
In600 - InA = 0.5115
In(2*3*10²) - InA = 0.5115
In2 + In3 + 2In10 - InA = 0.5115
0.693 + log3 * 2.303 + 2*2.303 - InA = 0.5115
0.693 + 0.477 * 2.303 + 2*2.303 - InA = 0.5115
InA = 5.886
logA * 2.303 = 5.886
logA = 2.556
logA = 2(0.301 + 0.477) + 1
logA = 2(log2 + log3) + log10
logA = 2log6 + log10
logA = log360
A = 360

(1) ln(1000/600)=k
(2) ln(600/A)=k
(1)=(2)
ln(1000/600)=ln(600/A)
1/360=1/A
A=360
這題是不需要先求k的，因為(1)同(2)的答案也是k的，求k的過程可以不管。