IB Maths AA SL AA 1.2 Exponents and logarithms questions

Exam-style questions in the shape of Paper 1 and Paper 2, with full markschemes. Read the markscheme, or type, photograph or draw your answer and get it marked.

Paper
Paper 1, no calculatorPaper 2, calculator
Difficulty
EasyMediumHard

Question 1

Paper 1, no calculatorMedium6 marks

Let p=log⁡23p=\log_2 3 and q=log⁡25q=\log_2 5 Consider the equation

4x+12=5×81343,x∈R.4^{x+\frac12}=\frac{5\times81^{\frac34}}{3},\qquad x\in\mathbb R.
(a)

Find the value of 813481^{\frac34}

[1]
(b)

Show that

log⁡2(5×81343)=2p+q.\log_2\left(\frac{5\times81^{\frac34}}{3}\right)=2p+q.
[2]
(c)

Hence solve the equation, giving your answer in terms of pp and qq

[3]

Question 2

Paper 2, calculatorMedium6 marks

Two account balances, in dollars, are modelled for t≥0t\geq 0 years after opening by

A(t)=240(1.04)t,B(t)=300(1.025)t.A(t)=240(1.04)^t,\qquad B(t)=300(1.025)^t.
(a)

Determine the time, in years, at which the two modelled balances are equal. Give your answer correct to two decimal places.

[4]
(b)

Hence determine the first whole number of years after opening at which A(t)>B(t)A(t)>B(t)

[2]

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