Which of the following is the value of log88

Question

log
⁡
88
, if log8≈0.9031
log
⁡
8
≈
0.9031
and log11≈1.0414
log
⁡
11
≈
1.0414
?(1 point)
Responses

log88≈0.9405
log
⁡
88
≈
0.9405
log 88 almost equal to 0 point 9 4 0 5

log88≈1.9445
log
⁡
88
≈
1.9445
log 88 almost equal to 1 point 9 4 4 5

log88≈1.1531
log
⁡
88
≈
1.1531
log 88 almost equal to 1 point 1 5 3 1

log88≈0.1383

Answer 1

To find the value of \( \log 88 \), we can use the change of base formula and the given values of \( \log 8 \) and \( \log 11 \).

Using the properties of logarithms, we can express \( 88 \) as \( 8 \times 11 \): \[ \log 88 = \log (8 \times 11) = \log 8 + \log 11 \]

Given:

• \( \log 8 \approx 0.9031 \)
• \( \log 11 \approx 1.0414 \)

Now substituting the values: \[ \log 88 \approx 0.9031 + 1.0414 \]

Calculating this sum: \[ \log 88 \approx 0.9031 + 1.0414 \approx 1.9445 \]

Thus, the value of \( \log 88 \) is approximately: \[ \log 88 \approx 1.9445 \]

So the correct response is: \[ \log 88 \approx 1.9445 \]