solve each equation for "x"by using the natural logarithm function. Round your answers to the nearest hundredth. Show work and describe
0.42^(-x)=7
2007-11-04 03:16:00 · 7 answers · asked by hockeyman25158 2 in Science & Mathematics ➔ Mathematics
take the ln of both sides:
ln (.42^(-x)) = ln 7
using logarithm rules, the -x part becomes a coefficient...
-x ln (.42) = ln 7
divide both sides by ln.42
-x *ln .42 / ln.42 = ln 7 / ln.42
-x = ln 7 / ln.42
x = -ln 7 / ln.42
x = 2.24
2007-11-04 03:23:48 · answer #1 · answered by sayamiam 6 · 0⤊ 0⤋
0.42^(-x)=7
take natural logrithms of both sides;
-xln(0.42)=ln7
x=-[ln7/ln0.42]
=-[1.9459/-0.8675]
=+2.2431.
= 2.2431=2.24 approx to nearest hundredth.ANS.
Verify:0.42^2.2431=0.14286
0.42^-2.2431= reciprocal of 0.14286=6.99986 OK.
2007-11-04 03:40:41 · answer #2 · answered by Anonymous · 0⤊ 0⤋
0.42^(-x)=7
Take nat. log of both sides
ln (0.42^(-x)) = ln (7)
- x ln(0.42) = ln (7)
- x ln (0.42) = ln (7)
x = - ln (7)/ln (0.42)
x = 2.24 << answer
2007-11-04 03:27:20 · answer #3 · answered by Shh! Be vewy, vewy quiet 6 · 0⤊ 0⤋
log answer/log base=exponent
log 7/log .42=-x
about -2.243=-x
x=about 2.243
2007-11-04 03:27:27 · answer #4 · answered by Harris 6 · 0⤊ 0⤋
0.42^(-x)=7
(-x) Ln 0.42 = Ln 7
-x = (Ln 7)/(Ln 0.42)
-x = 1.946/(-0.8675)
x = 2.243
.
2007-11-04 03:25:14 · answer #5 · answered by Robert L 7 · 0⤊ 0⤋
ln ( .42^(-x)) = ln7
x(ln (.42^-1)) = ln7
-x=ln7/(ln2.3)
x =ln(7-2.3)=ln4.7= 1.54
2007-11-04 03:30:25 · answer #6 · answered by Freddie 2 · 0⤊ 0⤋
ln(0.42^(-x)) = ln(7)
(-x)ln(0.42) = ln(7)
-x = ln(7) / ln(0.42)
x= 2.24 (2.dp)
2007-11-04 03:22:04 · answer #7 · answered by Anonymous · 0⤊ 1⤋