logarithm | MathCelebrity Forum

# logarithm

1. ### If p = log2(x), what is the value of log2(2x^3) in terms of p?

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
2. ### Simplify log(4) + log(12)

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. ### 3 power to what gets me 81

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
4. ### Farmer Yumi has too many plants in her garden. If she starts out with 150 plants and is losing them

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...
5. ### A population grows at 6% per year. How many years does it take to triple in size?

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...
6. ### Determine whether the statement is true or false. If 0 < a < b, then Ln a < Ln b

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...
7. ### Determine whether the statement is true or false. You can always divide by e^x

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.
8. ### A certain Illness is spreading at a rate of 10% per hour. How long will it take to spread to 1,200 p

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...
9. ### if Logb(5)=3.56 and logb(8)=4.61 then what is logb(40)

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
10. ### log5 = 0.699, log2 = 0.301. Use these values to evaluate log40

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...