My number is between 1 and 100. It is composite and one of its factors is 8. The number in the tens place is a prime number. The number in the ones place only has four factors (1, itself, and two other numbers). What is my number?

Numbers between 0 and 9 that have four factors are 6 and 8. So the number in the ones place is either 6 or 8.

Prime numbers between 0 and 9 are : 2, 3, 5 and 7.

The only combination of those numbers that has a factor of 8 would be 56

(56/7 = 8)

The number is 56

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: