Solve for t
100 x (1/2)^t/3.8
To solve for t in the equation 100 x (1/2)^(t/3.8), you can follow these steps:
Step 1: Divide both sides of the equation by 100:
(1/2)^(t/3.8) = 1
Step 2: Take the logarithm of both sides of the equation. Since the base of the exponent in the equation is (1/2), it's convenient to use the logarithm with base (1/2).
logbase(1/2)(1/2)^(t/3.8) = logbase(1/2)(1)
Step 3: Apply the logarithmic property that states logbase(b)(b^x) = x, which means the logarithm base b of b raised to any power is equal to that power.
t/3.8 = logbase(1/2)(1) = 0
Step 4: Multiply both sides of the equation by 3.8 to isolate t.
t = 0 x 3.8 = 0.
Therefore, the value of t that solves the equation 100 x (1/2)^(t/3.8) = 1 is t = 0.