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
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...
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...