solve the equation:
6P=Pe^1.1t
divide by P
6 = e^(1.1t)
take ln of both sides
ln 6 = ln (e^1.1t)
ln 6 = 1.1t(lne) , but lne = 1
t = ln6/1.1 = appr. 1.63
thanks!
To solve the equation 6P = P * e^(1.1t), where P is a constant and e is the mathematical constant approximately equal to 2.71828, we can follow these steps:
Step 1: Divide both sides of the equation by P:
(6P) / P = (P * e^(1.1t)) / P
Simplifying, we have:
6 = e^(1.1t)
Step 2: Take the natural logarithm (ln) of both sides of the equation:
ln(6) = ln(e^(1.1t))
Using the logarithmic property ln(a^b) = b * ln(a), we can rewrite the equation as:
ln(6) = 1.1t * ln(e)
Since ln(e) is equal to 1, we have:
ln(6) = 1.1t
Step 3: Finally, solve for t by dividing both sides of the equation by 1.1:
ln(6) / 1.1 = t
Using a calculator or any software that can compute natural logarithms, evaluate ln(6) / 1.1 to find the value of t. This will give you the solution to the equation.