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

1.

2log(base 2)x + log(base 2)5 = 4

log(base 2)x^2 + log(base 2)5 = 4 (The 2 in front becomes an exponent)

log(base 2)5*x^2  = 4                   (Same base, so you can multiply the two arguments together and put it all under a log(base 2))

5*x^2 = 16                                  (By definition of log, note 16 = 2^4)

x^2 = 3.2                                    (divide)

x = root(3.2)                                

Just plug it back into your calculator to check.

2.

Probability = Probablility it happens/ All possible outcomes

So, the the number of ways you can get 20 is ( 17 + 3, and 12 +8) so just 2 ways.

You can pick 2 numbers of the 6 in 15 ways.

So the probability that randomly picking 2 numbers that add up to 20 from that set is 2/15.

Hope that helps.