the log(10^ -1)of 3.66 =
of 9.86 =
of -2.8 =
thank you
To solve logarithmic expressions like log(10^(-1)) of 3.66, log(10^(-1)) of 9.86, and log(10^(-1)) of -2.8, we need to understand the properties of logarithms.
First, let's review the basic property of logarithms:
The logarithm with base "b" of a number "x" is written as logₐ(x) and represents the exponent to which "b" must be raised to equal "x" (i.e., b^(logₐ(x)) = x). In these examples, the base is 10: log(x) = log₁₀(x).
Now, let's solve the given expressions one by one:
1. log(10^(-1)) of 3.66:
Using the logarithmic property log(b^m) = m * log(b), we can rewrite the given expression as -1 * log(10) of 3.66.
Since log(10) is equal to 1 (because 10^1 = 10), we have:
-1 * 1 = -1.
Therefore, log(10^(-1)) of 3.66 is equal to -1.
2. log(10^(-1)) of 9.86:
Using the same property as above, we rewrite the given expression as -1 * log(10) of 9.86.
Again, log(10) is equal to 1, so we have:
-1 * 1 = -1.
Therefore, log(10^(-1)) of 9.86 is also equal to -1.
3. log(10^(-1)) of -2.8:
Applying the property, we rewrite this expression as -1 * log(10) of -2.8.
Now, the logarithm of a negative number is undefined in the real number system. Therefore, we cannot compute log(10) of -2.8.
Hence, the expression log(10^(-1)) of -2.8 is undefined.
In summary:
- log(10^(-1)) of 3.66 = -1
- log(10^(-1)) of 9.86 = -1
- log(10^(-1)) of -2.8 = undefined