On January 1, Olga started a new workout routine in which she rests every fourth day. On the same day, Nadia started a new workout routine in which
she rests every fifth day. If they both rested on January 1, what is the next date
on which both Olga and Nadia will rest?

20

step-by-step explanation:

answer: answer is b.

[m < b = 120º]

step-by-step explanation:

answer: it is 8

step-by-step explanation:

you know why its 8

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: