Exponentials and logarithms

WMA12Topic 2.53 questions

Exponential graphs, laws of logarithms and solving equations of the form $a^x = b$ .

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Original practice questions written in the style of the exam.

Question 15 marks
Solve the equation $\log_3 x + \log_3(x - 8) = 2$ .
Mark scheme
- M1 Uses the addition law: $\log_3\left(x(x - 8)\right) = 2$ (1)
- M1 Removes logs correctly: $x(x - 8) = 3^2$ (1)
Question 24 marks
Solve $2^{2x} - 5(2^x) + 6 = 0$ , giving any non-exact answer to 3 significant figures.

x (x - 8) = 3^{2}

A1

x^2 - 8x - 9 = 0

(1)

M1 Solves their quadratic:

(x - 9)(x + 1) = 0

(1)

A1

x = 9

only, rejecting

x = -1

because

\log_3

of a negative number is undefined (1)

Mark scheme