Question

Given that log(7) = 0.8451, find the value of the logarithm: log (1/7000)

Answer 1

The solution to the problem is as follows:

log(1/7000)

= log1 - log7000

= -log(7*10^3)

= -log7 + log10^3

= -log7 + 3

= 0.8451 + 3

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Answer 2

Answer: Hello there!

Let's use some relations:

log(a*b) = log(a) + log(b)

log(a/b) = log(a) - log(b)

log(1) = 0

log(a^b) = b*log(a)

now, we know that log(7) = 0.8451.

we want to finde log(1/7000)

log(1/7000) = log(1) - log(7000) = 0 - log(7000)

=- log(7*1000)

we can write 1000 as 10^3

=- (log(7) + log(10^3)) = -(0.8451 + 3*log(10))

and log(10) = 1

then we have:

-(0.8451 + 3*log(10)) = -(0.8451 + 3*1) = -3.8451