Question

Which of the following is the value of log 88
, if log 8 ≈ 0.9031 and log 11 ≈ 1.0414
(1 point)
Responses

log 88 ≈ 0.9405
log 88 ≈ 0.9405

log 88 ≈ 0.1383
log 88 ≈ 0.1383

log 88 ≈ 1.9445
log 88 ≈ 1.9445

log 88 ≈ 1.1531
log 88 ≈ 1.1531

1 answer

To find the value of \( \log 88 \), we can use the properties of logarithms. Specifically, we can break down \( 88 \) into its prime factors:

\[ 88 = 8 \times 11 \]

Using the property of logarithms that states \( \log(a \times b) = \log a + \log b \), we can write:

\[ \log 88 = \log(8 \times 11) = \log 8 + \log 11 \]

Now, we can substitute the values we have:

\[ \log 8 \approx 0.9031 \] \[ \log 11 \approx 1.0414 \]

Now, we will add these two values together:

\[ \log 88 \approx 0.9031 + 1.0414 = 1.9445 \]

Thus, the value of \( \log 88 \) is approximately \( 1.9445 \).

So the correct response is:

\[ \log 88 \approx 1.9445 \]