log 10^3 + log 10^-7
To simplify this expression, we can use the logarithm rule:
log(a) + log(b) = log(ab)
So, applying this rule to the given expression:
log(10^3) + log(10^-7) = log(10^3 * 10^-7)
Now, using the rule log(a^b) = b*log(a):
log(10^3 * 10^-7) = log(10^(3-7))
Simplifying the exponent:
log(10^(-4))
Since log(10^(-4)) represents the power to which 10 must be raised to equal 10^(-4), the result is -4.
Therefore, log(10^3) + log(10^-7) = -4.
To evaluate the expression log 10^3 + log 10^-7, we can use the properties of logarithms.
1. First, let's simplify each logarithm separately using the power rule of logarithms:
log 10^3 = 3 log 10
log 10^-7 = -7 log 10
2. Next, since log 10 equals 1, we can substitute this value into the above expressions:
3 log 10 = 3 * 1 = 3
-7 log 10 = -7 * 1 = -7
So now we have log 10^3 + log 10^-7 = 3 + (-7).
3. Finally, we can simplify the expression:
3 + (-7) = -4
Therefore, log 10^3 + log 10^-7 equals -4.