Question 1
Solve the equation $5e^{2x} - 3 = 12$ for $x$. Give your answer in exact form.
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Mathematical Methods Β· Unit 3 Β· Differentiation of exponential and logarithmic functions Β· Calculus of logarithmic functions
Solve equations involving exponential and logarithmic functions with base π, with and without technology.
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Question 2
Solve for \(x\) in the equation \(6e^{3x} - 5e^x = 3e^{-x}\).
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Question 3
A population of bacteria is modelled by the function \( N(t) = 1{,}200 e^{0.15t} \), where \( N \) is the number of bacteria and \( t \) is time in hours. Solve for the time \( t \) when the population reaches 4,800 bacteria.
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