10^0.475 = x / (0.0635 - x) Please help me and show the steps as much as possible. The answer is x = 0.0159.
2007-02-02 07:46:40 · 4 answers · asked by Daisy 1 in Science & Mathematics ➔ Mathematics
Well,
10^0.475=x/(0.0635-x)
log10^0.475=0.475=log{x/(0.0635-x)} --(1) because
there is a law that says log m=x always means that m=10^x; if log10^z=y,then 10^z=10^y where z is 0.475 and y=x/(0.0635-x).
From equation (1),
log{x/(0.0635-x)}=0.475
logx-log(0.0635-x)=0.475 {log(m/n)=logm-logn}
logx-log0.0635-(-logx)=0.475
logx-log0.0635+logx=0.475
logx+logx-log0.0635=0.475
2logx-log0.0635=0.475
2logx=0.475+log0.0635
Note: Use a log table from a log book OR a Calculator to get the value of log0.0635
log0.0635= -1.197226275
Therefore,
2logx=0.475+(-1.197226275)= -0.722226275
logx= (-0.722226275)/2= -0.361113137
Therefore,
logx= -0.361113137
x=10^ (-0.361113137) {Note:e.g 10^-x=1/(10^x)}
=1/{10^(0.361113137)}
=0.0476 (approximate)
0.0159 is a wrong answer.
2007-02-02 09:34:16 · answer #1 · answered by good day 2 · 0⤊ 0⤋
10^0.475 = x / (0.0635 - x)
10^0.475 (0.0635 - x) = x
0.0635*10^0.475 = (1 + 10^0.475)x
x = 0.0635*10^0.475 / (1 + 10^0.475)
x = 0.047567
x = 0.0159 is the wrong answer, you can see this if you plug it back into the original equation
2007-02-02 15:54:43 · answer #2 · answered by Anonymous · 0⤊ 0⤋
Multipliying by(0.0635-x) both sides
10^0.475(0.0635-x)=x As 10^0.475 = 2.9854 you get
0.1896 -2.9854x = x so x= 0.1896/3.9854 = 0.0476
2007-02-02 16:01:55 · answer #3 · answered by santmann2002 7 · 0⤊ 0⤋
10^.475 = 2.98538262 so...
2.985 * (.0635-x) = x
0.189571796 - 2.985 x = x
.1895 = 3.985 x
x = 0.0475667744
2007-02-02 15:52:55 · answer #4 · answered by slider 2 · 0⤊ 0⤋