Log Questions(Quick!)

2006-11-18 3:00 am
Give me Steps, Please!
1.5^3X-4×3^2X=7^X+1×11^2-X(X≒1.24)
2.4^X-4^X-1=192(X=4)

回答 (1)

2006-11-18 3:11 am
✔ 最佳答案
1.
5^(3X-4)×3^(2X)=7^(X+1)×11^(2-X)
log[5^(3X-4)×3^(2X)]=log[7^(X+1)×11^(2-X)]
log[5^(3X-4)] + log[3^(2X)]=log[7^(X+1)]+ log[11^(2-X)]
(3X-4) * log5 + (2X) * log3=(X+1) *log7+ (2-X) * log11
(3log5) * X-4 * log5 + (2log3) * X=log7* X + log7+ 2* log11 - log11 * X
(3log5 + 2log3 - log7+log11) * X= log7+ 2* log11 + 4 * log5
X= (log7+ 2* log11 + 4 * log5 ) / (3log5 + 2log3 - log7+log11) = 1.24
2.
4^X-4^X-1=192
4^X-(1/4) * 4^X=192
(1 - 1/4) * 4^X=192
(3/4) * 4^X=192
4^X=192 / (3/4) = 192 * 4 /3 = 256 = 4^4
X=4


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