Quick Question

In log(base of 1000) 0.1 , how exactly would you find x

Since 1000^x = 0.1 isn't really working.

Whar are you trying to solve:

=log 0.1
1000

since 10^3 = 1000,

10 = 1000^(1/3)
1/10 = 1000^(-1/3)
so, your log_1000(0.1) = -1/3

1000^x = 0.1
works just fine; you just have to know how to evaluate it.
x = -1/3

To find the value of x in the equation log(base 1000) 0.1, we can use the change of base formula. The formula states that log(base b) a = log(base c) a / log(base c) b, where c can be any positive number other than 1.

In this case, we can rewrite the equation log(base 1000) 0.1 as log(0.1) / log(1000). Here, we have changed the base to 10 since log(base 10) is commonly used.

Now, we can find the value of x by evaluating log(0.1) / log(1000) using a calculator.

log(0.1) โ‰ˆ -1 and log(1000) = 3. Therefore, x โ‰ˆ -1 / 3.

So, the value of x in the equation log(base 1000) 0.1 is approximately -1/3.