maths Log一問

log (base2n) 1944 = log (base n) 486*2^(1/2)
log_2n 1944 = log_n 486*2^(1/2)
log1944/log2n = log486*2^(1/2)) / logn
log1944/log486*2^(1/2) = log2n/logn
log_[486*2^(1/2)] 1944 = log_n n + log_n 2
log_n 2 = log [486*2^(1/2)] (1944/486*2^(1/2))
log2/logn = log [486*2^(1/2)] (1944/486*2^(1/2))
log2/log [486*2^(1/2)] (1944/486*2^(1/2)) = logn
10^{log2/log [486*2^(1/2)] (1944/486*2^(1/2))} = n
n = 77.9 (corr to 3 sig fig)

log2n_1944=logn_[486*2^(1/2)]
Sol
log2n_1944=logn_[486*2^(1/2)]
log1944/log(2n)=log[486*2^(1/2)]/logn
log[(2^3)*(3^5)]/log(2n)=log[2*(3^5)*2^(1/2)]/logn
(3log2+5log3)/(log2+logn)=[log2+5log3+(1/2)log2]/logn
(6log2+10log3)/(log2+logn)=(3log2+10log3)/logn

2010-10-25 08:18:04 補充：
(6log2+10log3)/(log2+logn)=(3log2+10log3)/logn
=(6log2+10log3-3log2-10log3)/(log2+logn-logn) 合分比
(6log2+10log3)/(log2+logn)=(3log2+10log3)/logn=3log2/log2=3
(3log2+10log3)/logn=3
3logn=3log2+10log3
n^3=[(2^3)*(3^10)]
n=54*3^(1/3)

log 1944 (base 2n) = log 486 x 2^(1/2) ( base n)
log 1944/log 2n = log 486 x 2^(1/2) / log n
3.2886/( log 2 + log n) = 2.83715/log n
3.2886 log n = 2.83715 x log 2 + 2.83715 log n
(3.2886 - 2.83715) log n = 0.854067
log n = 0.854067/0.45145 = 1.89183
n = 78.