If (0.2)x = 2 and log 2 = 0.3010, then the value of x to the nearest tenth is:
(a) -10.0, (b) -0.5, (c) -0.4, (d) -0.2, (e) 10.0
correct Option and Explain....
Answers
(0.2)x = 2.
Taking log on both sides
log (0.2)x = log 2.
x log (0.2) = 0.3010, [since log 2 = 0.3010].
x log (2/10) = 0.3010.
x [log 2 - log 10] = 0.3010.
x [log 2 - 1] = 0.3010,[since log 10=1].
x [0.3010 -1] = 0.3010, [since log 2 = 0.3010].
x[-0.699] = 0.3010.
x = 0.3010/-0.699.
x = -0.4306….
x = -0.4 (nearest tenth)
Answer: (c)
Hope it helps
Answer:
Explanation:
If I write ‘log 2’ it means that log 2 is a number which if made an exponent of base in above log will give us the number 2. Let me explain it a bit more. Log 2 is a number which if I raise to exponent of 10 will give me 2.
Since question says, 0.2x=2. What is the meaning of this Mathematical Statement? It means that if a make x a exponent of 0.2 I will get the number 2. Let us write it as a logarithm.
As a logarithm it will look like this;
Log(0.2)2=x
0.2 is the base of log.
If you have read about logrithms you might have heard of a rule called change of base rule.
In change of base rule if we a log whose base is a number other than 10 then we can convert that log into other with a base of 10 which make it easier to work with.
In above Mathematical Statement that we wrote base of log is 0.2 which is not 10 thus to change it to 10 we can do following things:
We have our logarithm as follows;
Log(0.2)2=x
=>(log2)/(Log0.2) [ change of base.]
To make base of a log equal to 10 we take its non-10 base and make it another log and divide it to the first log which is taken to base 10.
Now, back to question:
Log(0.2)2=x=>(log2)/(log0.2)
Since, log2 is given as 0.3010 and log0.2 can be calculated to be 0.699…
Putting above values we get:
0.3010/.699 = 0.43..
Hence answer is 0.43