Mathematical Methods — Question 15

QCAA 2020, Paper 1 · 4 marks

Q15 · 2020 · Technology-freeSimple familiar4 marks

QUESTION 15 (4 marks)

Solve the following equations.

4e^x=100

[1 mark]

2\log_4x-\log_4(x-1)=1

[3 marks]

WORKED SOLUTION

4 marks

ANSWER

x=\ln(25)

; b)

x=2

Worked solution

e^x=25

, hence

x=\ln(25)

b) Using log laws,

\log_4\left(\frac{x^2}{x-1}\right)=1.

Therefore

x^2/(x-1)=4

, so

x^2-4x+4=0

and

x=2

correctly determines

x

[1 mark]

correctly establishes equation using log laws

[1 mark]

correctly establishes the quadratic equation

[1 mark]

determines

x

[1 mark]

One QCAA sample method typeset for web; criterion wording is adapted from the official marking guide.

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