Log√0.000562
The mathematical expression "Log√0.000562" is not well-defined because the square root (√) of a negative number is not a real number. The square root function is only defined for non-negative real numbers. Therefore, the logarithm of √0.000562 cannot be computed.
To find the logarithm of √0.000562, we can follow these steps:
Step 1: Simplify the expression
√0.000562 can be written as √(5.62 × 10^(-4))
Step 2: Apply the logarithmic property
Logarithms can be used to convert multiplication into addition, so we can rewrite the expression as:
log(√(5.62 × 10^(-4))) = 1/2 * log(5.62 × 10^(-4))
Step 3: Use the logarithmic rule
We can use the logarithmic rule, log(ab) = log(a) + log(b), to simplify further:
1/2 * (log(5.62) + log(10^(-4)))
Step 4: Simplify the logarithms
log(10^(-4)) can be simplified using another logarithmic rule, log(a^n) = n * log(a):
1/2 * (log(5.62) - 4 * log(10))
Step 5: Evaluate the logarithms
log(10) = 1 (since 10 raised to the power of 1 equals 10), so the expression becomes:
1/2 * (log(5.62) - 4 * 1)
Step 6: Continue simplifying
1/2 * (log(5.62) - 4) = 1/2 * log(5.62) - 2
So, the logarithm of √0.000562 is 1/2 * log(5.62) - 2.
To evaluate the logarithm of √0.000562, you can use the properties of logarithms. Specifically, you can use the property log(a√b) = (1/2)log(a) + log(b), where a is the base of the logarithm.
Step 1: Simplify the expression
√0.000562 can be written as 0.000562^(1/2).
Step 2: Use the property of logarithms
We have log(0.000562^(1/2)) = (1/2)log(0.000562).
Step 3: Evaluate the logarithm
Since you didn't specify the base of the logarithm, I will assume it is base 10 (logarithm with no subscript usually refers to base 10 logarithm).
Using a calculator or math software, evaluate log(0.000562) to get an approximate value.
Therefore, the expression log(√0.000562) is equal to approximately (1/2) * (-3.250) = -1.625.