Please help me with these math problems?

Question

First day of school and already math hw with logariticim equations and probablity....

Can someone please help me?

1. Solve equation: 2log(base2)X+ log(base 2) 5= 4

2. probabiltiy of event: given the 2 numbers (3,8,11,12,17,19) find the probability that if two numbers are chosen at random, their sum will be 20.

thanks!! :)

Answer 1

il help but itl cost u

Answer 2

2log(base2)X + log(base2)5 =4

log(base2)x^2 + log(base2)5 =4

log(base2)5x^2 = 4

5x^2 =2^4

x^2 = 2^4/5

x = SQRT(2^4)/SQRT(5) = 2^2/SQRT(5) = 4/SQRT(5)

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Total combinations = 6*5 =30

Combinations that add to 20 are: 3,17; 17,3; 8,12; 12,8 =>4

so probability of adding to 20 is 4/30 = 2/15

Answer 3

2log(base2)X+ log(base 2) 5= 4

log(base2)X^2+ log(base 2) 5= 4

log(base2)5X^2) = 4

5x^2 = 2^4 = 16

x = 4/sqrt(5) = .8sqrt(5)

Two numbers whose sum is 20 are:

3+17, 8+12, 12+8, 17+3 <-- 4 possibilities

Total possibilities is 6P2 = 6!/4! = 30

So probability is 4/30 = 2/15 = 1/7.5