IB Questionbank

User interface language: English | Español

Date	November 2016	Marks available	5	Reference code	16N.1.AHL.TZ0.H_7
Level	Additional Higher Level	Paper	Paper 1	Time zone	Time zone 0
Command term	Solve	Question number	H_7	Adapted from	N/A

Question

Solve the equation ${4^x} + {2^{x + 2}} = 3$ .

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

attempt to form a quadratic in ${2^x}$ M1

${({2^x})^2} + 4 \bullet {2^x} - 3 = 0$ A1

${2^x} = \frac{{ - 4 \pm \sqrt {16 + 12} }}{2}{\text{ }}\left( { = - 2 \pm \sqrt 7 } \right)$ M1

${2^x} = - 2 + \sqrt 7 {\text{ }}\left( {{\text{as }} - 2 - \sqrt 7 < 0} \right)$ R1

$x = {\log _2}\left( { - 2 + \sqrt 7 } \right){\text{ }}\left( {x = \frac{{\ln \left( { - 2 + \sqrt 7 } \right)}}{{\ln 2}}} \right)$ A1

Note: Award R0 A1 if final answer is $x = {\log _2}\left( { - 2 + \sqrt 7 } \right)$ .

[5 marks]

Examiners report

[N/A]

Syllabus sections

Topic 1—Number and algebra » SL 1.5—Intro to logs

Show 28 related questions

22M.1.AHL.TZ1.12b:
Find the value of $b$ .
16N.1.SL.TZ0.S_9d:
Show that ${S_{12}} = 12{\log _2}x - 66$ .
22M.1.AHL.TZ1.12c:
Find the average number of earthquakes in a year with a magnitude of at least $7.2$ .
18M.2.SL.TZ1.S_8a:
Find the value of a and of b.
EXN.1.SL.TZ0.5b.i:
Write an expression for $C$ in terms of $p H$ .
22M.1.SL.TZ2.4a:
Calculate the pH of the coffee.
22M.1.SL.TZ2.4b:
Determine whether the unknown liquid is more or less acidic than the coffee. Justify your answer mathematically.
22M.1.SL.TZ1.11a:
Find the value of $a$ .
22M.1.SL.TZ1.11b:
Find the value of $b$ .
22M.1.SL.TZ1.11c:
Given $0 < M < 8$ , find the range for $N$ .
22M.1.AHL.TZ1.12a:
Find the value of $a$ .
16N.1.SL.TZ0.S_9b:
Show that the sum of the infinite sequence is $4{\log _2}x$ .
16N.1.SL.TZ0.S_9a:
Find $r$ .
18M.2.SL.TZ1.S_8b:
Use the regression equation to estimate the value of y when x = 3.57.
18M.1.AHL.TZ2.H_11c:
The region R, is bounded by the graph of the function found in part (b), the x-axis, and the lines $x = 1$ and $x = \alpha$ where $\alpha > 1$ . The area of R is $\sqrt 2$ .

Find the value of $\alpha$ .
18M.1.AHL.TZ1.H_5:
Solve ${\left( {{\text{ln}}\,x} \right)^2} - \left( {{\text{ln}}\,2} \right)\left( {{\text{ln}}\,x} \right) < 2{\left( {{\text{ln}}\,2} \right)^2}$ .
16N.1.SL.TZ0.S_9e:
Given that ${S_{12}}$ is equal to half the sum of the infinite geometric sequence, find $x$ , giving your answer in the form ${2^p}$ , where $p \in \mathbb{Q}$ .
18M.1.AHL.TZ2.H_11a:
Show that ${\text{lo}}{{\text{g}}_{{r^2}}}x = \frac{1}{2}{\text{lo}}{{\text{g}}_r}\,x$ where $r,\,x \in {\mathbb{R}^ + }$ .
18M.2.SL.TZ1.S_8c:
The relationship between x and y can be modelled using the formula y = kxⁿ, where k ≠ 0 , n ≠ 0 , n ≠ 1.

By expressing ln y in terms of ln x, find the value of n and of k.
17M.1.AHL.TZ1.H_1:
Find the solution of ${\log _2}x - {\log _2}5 = 2 + {\log _2}3$ .
18M.1.AHL.TZ2.H_11b:
Express $y$ in terms of $x$ . Give your answer in the form $y = p{x^q}$ , where p , q are constants.
16N.1.SL.TZ0.S_9c:
Find $d$ , giving your answer as an integer.
SPM.1.SL.TZ0.8a:
An orchestra has a sound intensity of 6.4 × 10⁻³W m⁻² . Calculate the intensity level, $L$ of the orchestra.
SPM.1.SL.TZ0.8b:
A rock concert has an intensity level of 112 dB. Find the sound intensity, $S$ .
18M.1.SL.TZ2.S_7b:
Let $p = {c^2}$ and $q = {c^3}$ . Find the value of $\sum\limits_{n = 1}^{20} {{u_n}}$ .
17N.1.AHL.TZ0.H_1:
Solve the equation ${\log _2}(x + 3) + {\log _2}(x - 3) = 4$ .
EXN.1.SL.TZ0.5a:
Find the $p H$ value for a solution in which the hydrogen ion concentration is $5.2 \times 10^{- 8}$ .
EXN.1.SL.TZ0.5b.ii:
Find the hydrogen ion concentration in a solution with $p H 4.2$ . Give your answer in the form $a \times 10 k$ where $1 \leq a < 10$ and $k$ is an integer.

Hide related questions

Topic 1—Number and algebra » AHL 1.9—Log laws

Topic 1—Number and algebra

Question

Markscheme

Examiners report

Syllabus sections

View options