Solve for p
93=12(2)^p
93=12(2)^p
2^p = 93/12 = 31/4
take logs
log 2^p = log (31/4)
p log2 = log31 - log4
p = (log 31 - log 4)/log 2
=
you push the buttons.
To solve for p in the equation 93 = 12(2)^p, we need to isolate the variable p. Here's how you can do it step by step:
1. Start by dividing both sides of the equation by 12 to get rid of the coefficient:
93/12 = (12(2)^p)/12
Simplifying:
7.75 = 2^p
2. Next, let's write 7.75 as a power of 2. Since 2^3 = 8 and 2^2 = 4, we know that 7.75 is between these two values.
7.75 is closer to 8, so we can write it as 2^(3 - 0.25):
7.75 ≈ 2^(2.75)
3. Now, we can equate the powers of 2:
2^p = 2^(2.75)
Since the bases are equal, we can set the exponents equal to each other:
p = 2.75
Therefore, the solution to the equation 93 = 12(2)^p is p = 2.75.