0.222 = (1.00583)^-n How do I solve for n?

Question

How do I use ln/log again? I used to know.. :(

Answer 1

Ln 0.222 = Ln (1.00583)^-n

Ln 0.222 = (-n)Ln (1.00583)

Ln 0.222/Ln 1.00583 = -n

-Ln 0.222/Ln 1.00583 = n

258.913 = n

Answer 2

matthew j's answer is correct; n = -log_1.00583(0.222), where the underscore indicates the base of the log. However, since these numbers are all decimals, I'm guessing you're expected to evaluate the expression, and you might not know how to do it. You need to use the change of base identity. The change of base simply states that log_a(b) = log_k(b) / log_k(a). That is, the log base a of b is equal to the log base k of b over the log base k of a, where k can be chosen arbitrarily. Your calculator doesn't have a log base 1.00583 button, but it should have an ln button or a log button (which normally means log_10). You can express -log_1.00583(0.222) as -ln(0.222) / ln(1.00583). suesysgoddess very cleverly reached this result directly; you should give her the points.

Answer 3

Your problem is equivalent to 0.222 = 1/1.00583ⁿ.

Thus we have 1.00583ⁿ = 1/0.222 which reduces to

n log (1.00583) = log (1/0.222)
n (0.0025245847947) = 0.653647025549
n = 0.653647025549 / 0.0025245847947
n = 258.912684145

You can use a scientific calculator to verify the answer.

Smile!

Answer 4

use log or natural logarithm ln
by raising each side of the equation with ln you can get
ln 0.222= -n *ln1.00583
by using a calculator u can calculate for n

Answer 5

take log to the base (1.00583) of both sides and u will get log to the base(1.00583) of 0.222 = -n

so n = -log base1.00583 of 0.222

Answer 6

0.222 = (1.00583)^-n
Ig 0.222 = lg (1.00583)^-n
lg 0.222 = -n(lg 1.00583)
n = -(lg 0.222/lg 1.00583)
n = 258.9126841...

Answer 7

Use log

Answer 8

a^-n = 1/a^n so

0.222=1/1.00583^n
0.222*(1.00583^n)=1