If log2 X + log4 X = 5, find X for the 3 decimal places.

Step-by-step explanation:

One is given the following expression:

Use the logarithm base change rule, which states the following:

Remember, a logarithm with not base indicated is another way of writing a logarithm to the base of (10). One can apply the base change rule to this situation:

Factor out (log(x)),

Inverse operations:

Simplify,

Now rewrite the logarithm, remember, a logarithm is another way of writing an exponent, in the following format:

Hello mate!

You have one $20 bill, two $10 bills, three $5 bills and four $1 bills in a bag.

This adds to a total of 10 bills in the bag, and you want to know the expected value if you took one at random.

The expected value is defined as ∑pₙxₙ

where pₙ is the probability for each event (in this case is the number of bills of a given price divided the number of bills in the bag) and xₙ is the value of the bill.

Then we can write the expected value as:

E = (1/10)*$20 + (2/10)*$10 + (3/10)*$5 + (4/10)*$1 = (1/10)( 20$ + 2*$10 + 3*$5 + 4*$1) = (1/10)*($59) = $5.90

The expected value is $5.90.