2007-03-27 00:03:14 · 6 answers · asked by Alan B 1 in Science & Mathematics ➔ Mathematics
Take logs (with base e) of both sides of the equation. Ln and exp are inverse functions of one another which means they will cancel each other out:
0.1 = exp(-3z)
ln[0.1] = ln[exp(-3z)]
ln0.1 = -3z
z = - (ln0.1)/3 (use calculator)
z = 0.767528
Hope this helps!
2007-03-27 00:06:10 · answer #1 · answered by M 6 · 2⤊ 1⤋
0.1=exp(-3z) both sides are positive
so you take the logarithms
ln(0.1)=-3z
z=ln(0.1)/-3
z=0.767528
2007-03-27 00:11:27 · answer #2 · answered by katsaounisvagelis 5 · 0⤊ 1⤋
take ln on both sides
=>ln(0.1) = ln exp(-3z)
=> ln(0.1) =-3z
=> z = -ln(0.1)/3
2007-03-30 21:34:58 · answer #3 · answered by sandy 2 · 0⤊ 0⤋
0.1 = exp(-3z),
take ln of each side;
ln(0.1)=ln(exp(-3z))
ln(0.1)=(-3z)
-3z=ln(1/10)= -ln(10)
z=ln(10)/3
=0.7675283643
i hope that this helps
2007-03-27 01:08:19 · answer #4 · answered by Anonymous · 0⤊ 1⤋
Take the natural log of both sides
ln(0.1) = -3z
z = -ln(0.1)/3
2007-03-27 00:08:55 · answer #5 · answered by dudara 4 · 0⤊ 1⤋
ln(0.1) = (-3z).ln(e)
- 2.3 = (-3z)
z = - 0.768
2007-03-27 06:16:11 · answer #6 · answered by Como 7 · 0⤊ 2⤋