Question

THe number of bacteria in an experiment can be represented by f(x)=4^x, where x represents the number of hours.
what is x when f(x)=64

Answer 1

To find the value of x when f(x) = 64, we can substitute 64 for f(x) in the given equation.

So, we have:

64 = 4^x

To solve for x, we can take the logarithm of both sides of the equation.

log(64) = log(4^x)

Using the property of logarithms which states that log(a^b) = b * log(a), we can rewrite the equation as:

log(64) = x * log(4)

Now, divide both sides of the equation by log(4):

x = log(64) / log(4)

Using a calculator:

x ≈ 3

Therefore, when f(x) = 64, x is approximately equal to 3.