Moderate -0.5 This is a straightforward logarithmic equation requiring a standard technique: take logs of both sides, apply log laws, collect terms in t, and solve. It's slightly easier than average because it's a direct application of a single method with no conceptual complications, though the algebraic manipulation requires care.
Apply logarithms to both sides and apply power law at least once
*M1
Obtain (4x+3)ln3=(2x+7)ln5
A1
Or equivalent with x not in a power.
Attempt solution of linear equation
DM1
Obtain 6.78
A1
Or greater accuracy.
4
Answer
Marks
Guidance
Question
Answer
Marks
Question 1:
1 | Apply logarithms to both sides and apply power law at least once | *M1
Obtain (4x+3)ln3=(2x+7)ln5 | A1 | Or equivalent with x not in a power.
Attempt solution of linear equation | DM1
Obtain 6.78 | A1 | Or greater accuracy.
4
Question | Answer | Marks | Guidance
Use logarithms to solve the equation $3^{4t+3} = 5^{2t+7}$. Give your answer correct to 3 significant figures. [4]
\hfill \mbox{\textit{CAIE P2 2024 Q1 [4]}}