Logaritmické rovnice
a) logx5 - logx4 + logx3=12
b)1 + log3 (5-x) - log3 (2x-1)=log3 (2x-1)
c)0,5 (3 log5 - 1 - logx)=2 - log5
b)1 + log3 (5-x) - log3 (2x-1)=log3 (2x-1)
c)0,5 (3 log5 - 1 - logx)=2 - log5
Odpovědi
Diskuze
log(x3*x5/x4)=12
log(x4)=12
x^4=10^12
x^4=10^(4*3)
x^4=(10^3)^4
x=(10^3)
x=1000
log 10 = 1
log3(3) = 1
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b)1 + log3 (5-x) - log3 (2x-1)=log3 (2x-1)
log3 (3) + log3 (5-x)/(2x-1)=log3 (2x-1)
(3)(5-x)/(2x-1)=(2x-1)
3(5-x)=(2x-1)*(2x-1)
(15-3x)=(4x^2-4x+1)
0=4x^2-x-14
(1+sqr(1+16*14))/8=x1
(1+sqr(225))/8=x1
(1+15)/8=x1
2=x1
(1-sqr(1+16*14))/8=x2
(1-sqr(225))/8=x2
(1-15)/8=x2
-14/8=x2
-7/4=x2
log5^3 - log 10 - logx = 2*2 - 2 log5
log5^3 - log 10 - logx + log5^2 = 2*2
log((5^3*5^2)/(10x)) = 4
log(5^5/(10x)) = 4
5^5/(10x) = 10^4
5^5/10^4 = 10x
5^5/10^5 = x
(5/10)^5 = x
(1/2)^5 = x
1/32 = x