2^x = (3/2)^6 solve for x
hint - take logs
2^x = 729/64
log 2^x = log (729/64)
x = log(729/64)/log2 = 3.5098
If a simple single-celled organism can reproduce by splitting in two every 7 hours. If you initially have 8 of these organisms, how many will you have in 35 hours?
Repost your question separately using "Post a New Question".
If you realize that 35 hours is seven "population doubling times" you should be able to answer it yourself.
What happens when you double 8 and then double the result six more times?
8*2*2*2*2*2*2*2 = _______
To solve the equation 2^x = (3/2)^6 for x, we can use logarithms.
1. Take the logarithm of both sides of the equation. We can choose any logarithm base, but a common choice is the natural logarithm (ln) or base 10 logarithm (log). Let's use the natural logarithm for this example.
ln(2^x) = ln((3/2)^6)
2. Apply the power rule of logarithms on both sides. This rule states that the logarithm of a number raised to an exponent is equal to the exponent multiplied by the logarithm of the number.
x * ln(2) = 6 * ln(3/2)
3. Divide both sides of the equation by ln(2) to isolate x.
x = (6 * ln(3/2)) / ln(2)
Now, using a calculator or approximation methods, you can evaluate the expression on the right side to find the value of x.