how to take out the log of 13 * 10 power 6please explain properly

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The first step is to write this number in scientific notation. Thus, 13 X 10^{6} will be written as 1.3 X 10^{7}. Next, we will take the log of the above number. Hence, we will have

log (1.3 X 10^{7}) = log 1.3 + log 10^{7}

[using log (ab) = log(a) + log(b)]

= log 1.3 + 7 log(10)

[using log(a)^{m} = m X log(a)]

Since log 10 = 1, hence 7 log(10) will be

= 7 X 1 = 7

Now, we will look the up the log table to find the value of log 1.3. The value corresponding to 13 in the log table is 1139. So, it will be reported as

log 1.3 = 0.1139.

Thus, the value of log 1.3 + 7 log(10) is

= 0.1139 + 7 = 7.1139

Hence the value of log 1.3 is 7.1139.

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