A bacterium in a petri dish multiplies by a factor of 5 every day. On day ,
there is 1 bacterium; on day 1, there are 5 bacteria, on day 2, there are
5.5= 25 bacteria; on day 3, there are 5.5.5=125 bacteria, and so on. What
logarithmic equation can be used to find the number of days it takes for a
colony of 1,000,000,000 bacteria to develop?

t = (ln 1,000,000,000)/ (ln 5)

from equation:  1,000,000,000 = 5^t

or you can translate:  t =  log of 1,000,000,000 with base 5

Step-by-step explanation:

We see the equation is   P =  5^t

where P = the number of bacteria

t = days

t = 0 day  we see P = 5^0 = 1 bacteria

so...

now you want t  when P= 1,000,000,000 bacteria

1,000,000,000 = 5^t

solve for t

t = (ln 1,000,000,000)/ (ln 5)

step-by-step explanation: