CAIE A-Level Mathematics A2 3.2.3 Log Equations Questions

Practise solving index equations by substitution, logarithms and equivalent exponential forms.

Exam points

Use log laws to form a linear equation in an exponent, giving an exact log ratio or requested rounding.
Convert to a quadratic using u = eˣ, reject non-positive roots, then use ln to find x.
Split a modulus exponential inequality into two bounds and state one combined interval.
Solve P = aeᵏᵗ for doubling time by cancelling a and taking logarithms of eᵏᵗ = 2.

[Maximum number: 4]

Solve the equation $4^{x-2}=4^{x}-4^{2}$ , giving your answer correct to 3 decimal places.

Use laws of indices correctly and solve for $4^{x}$
Obtain correct solution in any form, e.g. $4^{x}=\frac{256}{15}$
Use a correct method for solving an equation of the form $4^{x}=a$ , where
a>0
Obtain answer 2.047

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CAIE A-Level Mathematics A2 3.2.3 Log Equations Questions question 1