SOLUTION: i have to use logrithms to solve the folowing equation, correct to 4 significant figures 4=32(1-2x) the brackets are small if that makes a diference please tell me how you got t

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: i have to use logrithms to solve the folowing equation, correct to 4 significant figures 4=32(1-2x) the brackets are small if that makes a diference please tell me how you got t      Log On


   

Question 704768: i have to use logrithms to solve the folowing equation, correct to 4 significant figures 4=32(1-2x) the brackets are small if that makes a diference
please tell me how you got to your answer
Found 2 solutions by nerdybill, KMST:
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
4=32%5E%281-2x%29+
take log base 32 of both sides to get:
log%2832%2C4%29+=+log%2832%2C32%5E%281-2x%29%29+
on the right, it just reduces to:
log%2832%2C4%29+=+%281-2x%29+
apply "change of base" to the left:
log%284%29%2Flog%2832%29+=+1-2x+
log%284%29%2Flog%2832%29+-+1+=+-2x+
multiplying both sides by -1:
+-log%284%29%2Flog%2832%29+%2B+1+=+2x+
or
+1-log%284%29%2Flog%2832%29+=+2x+
dividing both sides by 2:
+%281-log%284%29%2Flog%2832%29%29%2F2+=+x+
+%281-0.4%29%2F2+=+x+
+%280.6%29%2F2+=+x+
+0.3+=+x+
to four significant places:
+0.3000+=+x+

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The part "correct to 4 significant figures" must have come from general instructions given for a test including many questions.
The instructions may have included using logarithms as needed, but logarithms are not needed to solve that equation.
4=32%281-2x%29 --> 4=32%2A1-32%2A2x applying the distributive property
4=32%2A1-32%2A2x --> 4=32-64x performing indicated multiplications
4=32-64x --> 4%2B64x-4=32-64x%2B64x-4 adding 64x-4 to both sides of the equal sign
4%2B64x-4=32-64x%2B64x-4 --> 64x%2B4-4=32-64x%2B64x-4 --> 64x=32-4 --> 64x=28
rearranging (commutative and associative properties) and doing indicated operations
The explanation for that step could get even more involved, if you wanted
64x=28 --> 64x%2F64=28%2F64 --> x=28%2F64 --> x=7%2F8
I do not need a calculator, or a slide rule, or logarithms to divide 7 by 8 to find the answer as a decimal.
I can calculate that in my head, without even paper and pencil, thinking this
7%2F8=1-1%2F8=1-1%2A125%2F%288%2A125%29=1-125%2F1000=1-0.1250000=0.8750000

USING LOGARITHMS:
I have not needed to use logarithms to divide since calculators were invented.
(I hope you are not expected to do that)
If it was a more complicated fraction/division, and I only had a table of base 10 logarithms, paper, and pencil, I would calculate 7%2F8 as a decimal correct to 4 significant figures like this:

Then, I would look in the table for the number that has 0.9420080 for a logarithm.
I would see that
log%288.74%29=0.9415114
log%288.75%29=0.9420081
log%288.76%29=0.9425041
Since the difference between consecutive logs is log%288.75%29-log%288.74%29=0.0004967 for numbers differing in 0.01,
if would not even try to interpolate to get a more accurate answer,
because I would figure (without even calculating it), that
log%288.749%29=0.9420081-0.01%2A0.000497=0.9420081-%280.001%2F0.01%29%2A0.0000497=0.9419584
is much farther than log%288.750%29 from 0.9420080.
So, highlight%28x=0.8750%29 is an answer correct to 4 significant figures.