Using logarithm table evaluate 4√0.007

Answer 1

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.