Question
Find x, if 10^logx=1/1,000
.(1 point)
x=
.(1 point)
x=
Answers
GPT 3.5
To solve this problem, we need to use the fact that log(x) is the inverse function of 10^x. This means that if 10^log(x) = y, then log(10^log(x)) = log(y).
Given that 10^log(x) = 1/1,000, we can write the equation as log(10^log(x)) = log(1/1,000).
Using the property that log(base a) (b) = c is equivalent to a^c = b, we can rewrite the equation as 10^log(x) = 1/1,000.
To simplify the equation further, we can rewrite 1/1,000 as 10^(-3), since 10^-3 is equal to 1/1,000.
Therefore, we have 10^log(x) = 10^(-3).
Since this equation has the same base, we can equate the exponents and solve for x:
log(x) = -3
Using the fact that 10^(-3) = 1/10^3 = 1/1,000, we can rewrite the equation as x = 1/1,000.
Therefore, the value of x is 1/1,000.
Given that 10^log(x) = 1/1,000, we can write the equation as log(10^log(x)) = log(1/1,000).
Using the property that log(base a) (b) = c is equivalent to a^c = b, we can rewrite the equation as 10^log(x) = 1/1,000.
To simplify the equation further, we can rewrite 1/1,000 as 10^(-3), since 10^-3 is equal to 1/1,000.
Therefore, we have 10^log(x) = 10^(-3).
Since this equation has the same base, we can equate the exponents and solve for x:
log(x) = -3
Using the fact that 10^(-3) = 1/10^3 = 1/1,000, we can rewrite the equation as x = 1/1,000.
Therefore, the value of x is 1/1,000.