Solve the equation log4P +logp 64 = 4
Question
Solve the equation log4P +logp 64 = 4
Solution
Sure, let's solve the equation step by step.
The given equation is log4P + logp64 = 4.
Step 1: Combine the logarithms using the product rule of logarithms. The product rule states that logb(MN) = logbM + logbN. So, we can rewrite the equation as log4(P*64) = 4.
Step 2: Convert the logarithmic equation to an exponential equation. The exponential form of logbM = N is b^N = M. So, we can rewrite the equation as 4^4 = P*64.
Step 3: Simplify the equation. 4^4 = 256 and 64P = 256.
Step 4: Solve for P. Divide both sides of the equation by 64 to isolate P. P = 256/64 = 4.
So, the solution to the equation log4P + logp64 = 4 is P = 4.
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