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

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) (Show Source): You can put this solution on YOUR website!

take log base 32 of both sides to get:

on the right, it just reduces to:

apply "change of base" to the left:

multiplying both sides by -1:

or

dividing both sides by 2:

to four significant places:

Answer by KMST(5328) (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.
--> applying the distributive property
--> performing indicated multiplications
--> adding to both sides of the equal sign
--> --> -->
rearranging (commutative and associative properties) and doing indicated operations
The explanation for that step could get even more involved, if you wanted
--> --> -->
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

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 as a decimal correct to 4 significant figures like this:

Then, I would look in the table for the number that has for a logarithm.
I would see that

Since the difference between consecutive logs is for numbers differing in ,
if would not even try to interpolate to get a more accurate answer,
because I would figure (without even calculating it), that

is much farther than from .
So, is an answer correct to 4 significant figures.
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