1/1024=42*0.5^(t/12.5)
Solve for t. Please show work. Much appreciated!
take log of each side.
-log1024=log42+t/12.3 * log 1/2
solve for t.
im getting 104 hours but the correct answer is 125 hours?
(-log1024-log42)12.5/log.5=192hrs
To solve for t in the equation 1/1024 = 42 * 0.5^(t/12.5), we can follow these steps:
Step 1: Isolate the exponential term 0.5^(t/12.5).
Divide both sides of the equation by 42:
(1/1024) / 42 = 0.5^(t/12.5)
Step 2: Simplify the left side of the equation.
To simplify (1/1024) / 42, we can multiply the numerator and denominator by 1/42:
(1/1024) / (42/1) = 1/(1024 x 42) = 1/43008.
So, the equation becomes: 1/43008 = 0.5^(t/12.5)
Step 3: Apply logarithms to both sides of the equation.
Taking the logarithm (base 0.5) of both sides will allow us to solve for t.
log0.5(1/43008) = log0.5(0.5^(t/12.5))
Step 4: Simplify the logarithm expression using the logarithmic identity.
According to the logarithmic identity, logb(b^x) = x, where b is the base.
Using this identity, we have:
log0.5(1/43008) = t/12.5
Step 5: Multiply both sides by 12.5 to solve for t.
Multiply both sides of the equation by 12.5:
12.5 * log0.5(1/43008) = t/12.5 * 12.5
log0.5(1/43008) = t.
Therefore, the solution for t is log base 0.5 of 1/43008.