Which of the following is the value of log86

Question

, if log2≈0.3010
and log43≈1.6335
?(1 point)
Responses

log86≈3.2670
logarithm 86 approximately equals 3.2670

log86≈1.9345
logarithm 86 approximately equals 1.9345

log86≈1.3325
logarithm 86 approximately equals 1.3325

log86≈0.4917

Answer 1

To find \( \log 86 \) using the given logarithmic values, we can express 86 in terms of the bases provided (logarithms base 2 and base 43):

1. Express 86 in prime factors:

   • We note that \( 86 = 43 \times 2 \).

2. Use the property of logarithms: \[ \log 86 = \log (43 \times 2) = \log 43 + \log 2. \]

3. Substituting the values:

   • From the problem, we have: \[ \log 2 \approx 0.3010, \] \[ \log 43 \approx 1.6335. \]
   • So, \[ \log 86 \approx 1.6335 + 0.3010 = 1.9345. \]

Thus, the value of \( \log 86 \) is approximately:

\[ \log 86 \approx 1.9345. \]

Therefore, the correct response is: logarithm 86 approximately equals 1.9345.