6/15
equals 0.40
to calculate, 15 divided by 6 equals 0.40.
The answer's at the bottom. Let me know if you have any questions
Answer:
is an extraneous solution: True
is the only solution: True
Step-by-step explanation:
The given logarithmic equation is: 
Apply the property 
to the LHS to get: 
We rewrite the corresponding indicial expression to get:
Simplify the RHS to get:
Take square root to get:
Since the domain of the logarithmic function is positive real numbers, the only solution is
Answer:
There are a total of 2011 integer divisors.
Step-by-step explanation:
The only primes p such that 1/p has finite spaces after the coma are 2 and 5. If we divide a number with last digit odd we will obtain 1 extra digit after the decimal point and if we divide a number by 5 we will obtain 1 more digit if that number has a last digit in the decimal which is not a multiple of 5.
If we take powers of those primes we will obtian one more digit each time. In order to obtain more digits it is convinient to divide by a power of 2 instead of a power of 5, because the resulting number will be smaller.
If we want 2010 digits after the decimal point, we need to divide 1 by 2 a total of 2010 times, hence f(2010) = 2²⁰¹⁰, which has as positive integer divisors every power of 2 between 0 and 2010, hence there are a total of 2011 integer divisors of f(2010).
