Using logarithm table evaluate 4√0.007
To evaluate 4√0.007 using a logarithm table, we can rewrite the expression as a power of 10 by using the properties of logarithms.
4√0.007 = 0.007^(1/4)
Now, we can take the logarithm of both sides of the equation to solve for the exponent.
log(4√0.007) = log(0.007^(1/4))
Using the logarithmic property log(a^b) = b*log(a), we can rewrite the equation as:
log(4√0.007) = (1/4) * log(0.007)
Now, we need to look up the logarithm of 0.007 in the logarithm table. Let's assume the logarithm of 0.007 is -2.154.
log(4√0.007) = (1/4) * (-2.154)
Simplifying further, we have:
log(4√0.007) = -0.539
Therefore, 4√0.007 is approximately equal to 10^(-0.539) using a logarithm table.
To evaluate 4th root of 0.007 using a logarithm table, follow these steps:
Step 1: Convert the given number into a decimal form:
0.007 can be written as 7/1000 or 7 × 10^(-3).
Step 2: Take the logarithm of the decimal form using the logarithm table:
log(7 × 10^(-3)) = log(7) - 3.
Step 3: Find the logarithm of 7 using the logarithm table:
log(7) = 0.8451.
Step 4: Substitute the values found in Steps 2 and 3 into the original equation:
4th root of 0.007 = 10^[(log(7) - 3)/4] = 10^[(0.8451 - 3)/4].
Step 5: Simplify the exponent:
10^[(0.8451 - 3)/4] = 10^(-1.1549/4) = 10^(-0.2887).
Step 6: Evaluate the expression using the logarithm table:
10^(-0.2887) = 0.6532.
Therefore, the 4th root of 0.007 is approximately 0.6532.