logarithm

If p = log2(x), what is the value of log2(2x^3) in terms of p? A. 6p B. 2p^3 C. 1 + 3p D. 3 + 3p E. 1 + p^3 log2(2x^3) = log2(2) + log2(x^3) log2(2) = 1, so we have: log2(2x^3) = 1 + 3log2(x) Since we're given log2(x) = p, we have: log2(2x^3) = 1 + 3p - Answer C

Answer Choices A) log(3) B) log(48) C) 16 D) log(8) E) log(16) We know that log(ab) = log(a) = log(b) Looking at our problem, we see that a = 4 and b = 12, so we have: log(4) + log(12) = log(4 * 12) log(4) + log(12) = log(48) Answer B

3 power to what gets me 81 Let x be our power: 3^x = 81 3 * 3 * 3 * 3 = 81 So x = 4: 3^4 = 81

Farmer Yumi has too many plants in her garden. If she starts out with 150 plants and is losing them at a rate of 4% each day, how long will it take for her to have 20 plants left? Round UP to the nearest day. We set up the function P(d) where d is the number of days sine she started losing...

A population grows at 6% per year. How many years does it take to triple in size? With a starting population of P, and triple in size means 3 times the original, we want to know t for: P(1.06)^t = 3P Divide each side by P, and we have: 1.06^t = 3 Typing this equation into our search engine to...

Determine whether the statement is true or false. If 0 < a < b, then Ln a < Ln b We have a logarithmic property that states: ln(a) - ln(b) = ln (a / b) We're given a < b, so (a / b) < 1 Therefore: ln (a / b) < 0 And since ln(a) - ln(b) = ln (a / b) Then Ln(a) - Ln(b) < 0 Add Ln(b) to...

Determine whether the statement is true or false. You can always divide by e^x True. As x --> infinity, 1/e^x approaches 0 but never touches it.

A certain Illness is spreading at a rate of 10% per hour. How long will it take to spread to 1,200 people if 3 people initially exposes? Round to the nearest hour. Let h be the number of hours. We have the equation: 3 * (1.1)^h = 1,200 Divide each side by 3: 1.1^h = 400 Type this equation...

if Logb(5)=3.56 and logb(8)=4.61 then what is logb(40) There exists a logarithmic identity which says log(xy) = log(x) + log(y). Since the two logs above have the same base b, we have: x = 5 and y = 8. So we have: logb(40) = logb(5) + logb(8) logb(40) = 3.56 + 4.61 logb(40) = 8.17

log5 = 0.699, log2 = 0.301. Use these values to evaluate log40. One of the logarithmic identities is: log(ab) = log(a) + log(b). Using the numbers 2 and 5, we somehow need to get to 40. List factors of 40. On the link above, take a look at the bottom where it says prime factorization. We...