If log c = -399.699, give the value of c in scientific notation without using any calculator. Show your work.
hint: the value of c is small but it does not equal to zero
Ahh another Lakeland student looking for answers. Damn this pre lab
We have this at the U of A too
To find the value of c in scientific notation without using a calculator, we need to understand the relationship between logarithms and exponentiation.
The logarithm of a number to a given base can be defined as the exponent to which the base must be raised to obtain that number. In this case, we have log c = -399.699.
To convert this to exponential form, we rewrite the equation as c = base^exponent. The base will be the same as the base of the logarithm, and the exponent will be the negative value of the logarithm.
So, c = 10^(-399.699).
Using the properties of exponents, we can rewrite the equation as c = 1 / 10^(399.699).
Now let's write 10^(399.699) without using a calculator. Start by noticing that 10 can be written as 10^1. This allows us to simplify the equation as c = 1 / (10^1)^(399.699).
Next, we apply the exponent rule that states (a^m)^n = a^(m * n). This allows us to rewrite the equation as c = 1 / 10^(399.699 * 1).
Since anything raised to the power of 1 is itself, we now have c = 1 / 10^399.699.
Finally, to express c in scientific notation, we can rewrite it as c = 1 / (10^3)^133.233.
Simplifying further, we have c = 1 / (1000)^133.233.
Since 1000 is equal to 10^3, we have c = 1 / (10^3)^133.233 = 1 / (10^399.699).
Hence, the value of c in scientific notation is approximately 1 x 10^(-399.699).
Disclaimer: idk if I'm right
base 10 both sides of log c = -399.699
you get c = 10^-399.699
I rounded -399.699 to -400
so you have c = 10^-400
so c = 1 x 10^-400
which is really small, but not zero.