Question 616610: 2 logu125+8=14
The u is smaller than the g and is the base. I keep struggling with this problem and your help is greatly appreciated. Thank you
Found 2 solutions by ewatrrr, Theo:
Answer by ewatrrr(24785)   (Show Source):
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! you mean (log(125) to the base of u) + 8 = 14?
that would look like this:
log(u,125) = 
from that, i gather that this problem is:
2*log(u,125) + 8 = 14 which would look like:
if that's what it is, then the solution would be as follows:
subtract 8 from both sides of the equation to get:
2*log(u,125) = 14 - 8 which becomes:
2*log(u,125) = 6
divide both sides of this equation by 2 to get:
log(u,125) = 3
by the laws of logarithms log(b,x) = y if and only if b^y = x
based on this, your problem then becomes:
log(u,125) = 3 if and only if u^3 = 125
take the cube root of both sides of this equation to get:
u = (125)^(1/3)
the cube root of 125 should be 5 because 5^3 = 125.
if you didn't know that, you would use your calculator to solve for u to get:
u = (125)^(1/3) = 5
to confirm this is correct, use that value of u to solve the original equation.
the original equation is:
2*log(u,125) + 8 = 14
since u = 5, this becomes:
2*log(5,125) + 8 = 14
you can use the log base conversion formula to make this equivalent to:
2*log(10,125)/log(10,5) + 8 = 14
since the LOG function of your calculator already solves for logs to the base of 10, your equation becomes:
2*LOG(125)/LOG(5) + 8 = 14
you can now use your calculator to solve this equation to get:
14 = 14 confirming that the value of 5 for u is good.
the log conversion formula is:
log(b,c) = log(d,c)/log(d,b)
what this says is that the log of c to the base of b is equal to:
the log of c to the base of d divided by the log of b to the base of d.
c is the original number that you want to get the log of.
b is the original base.
d is the new base.
you take the log of the same number to the base of d (the new base) and divide that by the log of b (the old base) to the base of d (the new base).
in solving a problem like this, you need to know the basic definition of logarithms that states:
log(b,x) = y if and only if b^y = x
in symbolic notation, this would look like this:
 if and only if 
here's a reference that explains that in possibly a more elegant fashion than i could.
http://www.themathpage.com/aprecalc/logarithms.htm
|
|
|
