Which of the following is the value of log88, if log=0.9031 and log11=1.0414?

Question

1)log88=0.1383
2)log88=1.1531
3)log88=0.9405
4)log88=1.9445

Answer 1

To calculate \(\log_{10} 88\) using the values provided for \(\log 8\) and \(\log 11\), we can use the property of logarithms that states:

\[ \log_{10} (a \cdot b) = \log_{10} a + \log_{10} b \]

First, we factor 88 into its prime factors:

\[ 88 = 8 \cdot 11 \]

Thus, we can express \(\log_{10} 88\) as:

\[ \log_{10} 88 = \log_{10} 8 + \log_{10} 11 \]

Given that \(\log_{10} 8 = 0.9031\) and \(\log_{10} 11 = 1.0414\), we can now calculate \(\log_{10} 88\):

\[ \log_{10} 88 = 0.9031 + 1.0414 \]

Calculating this:

\[ \log_{10} 88 = 1.9445 \]

Now we can match this result with the options provided:

1. \(\log 88 = 0.1383\)
2. \(\log 88 = 1.1531\)
3. \(\log 88 = 0.9405\)
4. \(\log 88 = 1.9445\)

The correct value \( \log 88 = 1.9445 \) corresponds to option 4.

Thus, the answer is:

4) log 88 = 1.9445