Question 560307: v=e^(w/pz)
Find w when v=15, p=1.2, z=34
i cant work out how to transpose this formula using logarithms to make part of the exponent (W) the subject.
I=log(2,(1/p))
Find P when I=4
similar problem of being unable to separate the exponent to make it the subject
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! your first problem is interpreted as follows:
the original equation i:
v=e^(w/pz)
Find w when v=15, p=1.2, z=34
substituting these values into your equation, you get:
15 = e^(w/(1.2*34)
simplify this to get:
15 = e^(w/40.8)
take the natural log of both sides of this equation to get:
ln(15) = ln(e^(w/40.8)
note that ln means log to the base of e
example:
ln(x) means log of x to the base of e.
that could also be shown as log(e,x)
anyway, you take the natural log of both sides of the equation to get:
ln(15) = ln(e^(w/40.8)
by the rules of logarithms, log(x^y) = y * log(x)
in your equation, y = (w/40.8) and x = e and log = ln
using this rule, your equation becomes:
ln(15) = (w/40.8) * ln(e)
since ln(e) is equal to 1, your equation becomes:
ln(15) = (w/40.8)
multiply both sides of this equation by 40.8 to get:
w = ln(15) * 40.8
use your calculator to solve for w to get:
w = 110.4884482
substitute for w in your original equation to get:
original equation is:
v=e^(w/pz)
after substitution of all known values, equation becomes:
15 = e^(110.4884482/(1.2*34)
simplify this to get:
15 = e^(110.4884482/40.8)
simplify further to get:
15 = e^(2.708050201)
simplify further to get:
15 = 15
this confirms the answer is good.
ln means natural log and is usually the LN function key on your calculator.
-----
my interpretation of your second problem equation is:
I=log(2,(1/p))
this means the log of (1/p) to the base of 2.
assuming this interpretation is correct, you would solve this as follows:
original equation is:
I = log(2,(1/p))
Find p when I=4
if your replace I with 4, then your equation becomes:
4 = log(2,(1/p))
in general, y = log(b,x) if and only if b^y = x
in your equation, b is equal to 2 and x is equal to (1/p) and y is equal to 4.
using this rule, your equation becomes:
4 = log(2,(1/p)) if and only if 2^4 = (1/p)
simplify this equation to get:
16 = (1/p)
multiply both sides of this equation by p to get:
16*p = 1
divide both sides of this equation by 16 to get:
p = 1/16
substitute for p in your original equation to see if it holds true.
your original equation is:
I=log(2,(1/p))
substitute 4 for I and (1/16) for p to get:
4 = log(2,(1/(1/16))
simplify this to get:
4 = log(2,16)
you can use your calculator to solve for log to the base of 2 as follows:
log(2,16) = log(16)/log(2)
your equation becomes:
4 = log(16)/log(2) which is simplified to:
4 = 3
this confirms the fact that p = (1/16) is a good value.
|
|
|
