A bacterium in a petri dish multiplies by a factor of 2 every day. On day O, there is 1 bacterium; on day 1, there are 2 bacteria, on day 2, there are 2•2 = 4 bacteria; on day 3, there are 2•2•2=8 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?

A: 1,000,000,000x = log10 2

B: 1,000,000,000 = log2 x

C: x= log2 1,000,000,000

D: x^2 = log10 1,000,000,000

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation: