Using logarithm table evaluate 4√0.007
To evaluate 4√0.007 using a logarithm table, we can use the property that states √a = a^(1/2). Therefore, 4√0.007 can be written as 4(0.007)^(1/2).
Taking the logarithm of both sides, we have:
log(4√0.007) = log[4(0.007)^(1/2)]
Using the property log(ab) = log(a) + log(b), we can rewrite the expression as:
log(4) + log[(0.007)^(1/2)]
Now, let's use the logarithm table for log(4) and log(0.007). Assuming the table provides logarithmic values for numbers less than 1, we can find that:
log(4) = 0.6021 (approx)
log(0.007) = -2.1549 (approx)
Therefore, our expression becomes:
0.6021 + log[(0.007)^(1/2)]
Using the property log(a^n) = n*log(a), the expression simplifies to:
0.6021 + (1/2) * log(0.007)
Now, using the logarithm table for log(0.007), which is -2.1549 (approx), we can calculate:
0.6021 + (1/2) * (-2.1549)
This simplifies to:
0.6021 - 1.0775 = -0.4754
Therefore, the value of 4√0.007 using a logarithm table is approximately -0.4754.
To evaluate 4√0.007 using a logarithm table, we can follow these steps:
Step 1: Convert 4√0.007 to exponent form.
We have 4√0.007 = (0.007)^(1/4)
Step 2: Take the logarithm of both sides.
Let's take the logarithm (base 10) of both sides:
log((0.007)^(1/4)) = log(4√0.007)
Step 3: Apply the logarithm rules.
Using the property log(a^b) = b * log(a), we can rewrite the equation as:
(1/4) * log(0.007) = log(4)
Step 4: Evaluate the right side of the equation using the logarithm table.
Look up the logarithm of 4 in the table.
The logarithm of 4 is 0.6021.
Step 5: Solve for the left side of the equation.
Now we need to solve for (1/4) * log(0.007).
Using the logarithm table, look up the logarithm of 0.007.
The logarithm of 0.007 is -2.1549.
Then, compute (1/4) * (-2.1549):
(1/4) * (-2.1549) = -0.5387
So, (1/4) * log(0.007) is approximately -0.5387.
Step 6: Substitute the values back into the original equation.
Substituting the values back into the original equation, we have:
-0.5387 = 0.6021
Step 7: Evaluate the left side of the equation.
We can solve for (-0.5387) by referring to the logarithm table.
The number closest to -0.5387 in the table is -0.5376, which corresponds to 0.3031.
Therefore, the value of 4√0.007 evaluated using a logarithm table is approximately 0.3031.