Logarithmus to simple subtraction - how? I am learning for a math exam and have the following solut

Carla Jenkins

Carla Jenkins

Answered question

2022-06-02

Logarithmus to simple subtraction - how?
I am learning for a math exam and have the following solution:
0.01 = 0.5 n n log 0.5 = log 0.01 n = log 0.01 log 0.5
OK, so far, so good. (I guess)
But now, it gets weird:
n = log 0.01 log 0.5 = 0 2 0.7 1 =
Can somebody please explain how to go from log 0.01 to 0 2 and from log 0.5 to 0.7 1

Answer & Explanation

rederijkd6h1c

rederijkd6h1c

Beginner2022-06-03Added 3 answers

For the numerator, notice that .01 = 1 100 and by logarithmic rules
log .01 = log 1 100 = log 1 log 100 = 0 2
The same goes for the denominator: .5 = 5 10
log .5 = log 5 10 = log 5 log 10 = 0.7 1
Using the logarithmic rule:
log a ( m n ) = log a m log a n
Andres Durham

Andres Durham

Beginner2022-06-04Added 1 answers

log 0.01 = log(1/100) = log 1 - log 100 = log 1 - 2 log 10 = 0-2
log 0.5 = log(2/10) = log 2 - log 10 = 0.7 - 1
log(a/b) = log a -log b
log(a^n) = n log a
Hope this helps!

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