Why isn't the answer to TMUA-P1X-MM5-02 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1X-MM5-02 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1X-MM5-02?

No — calculators are banned in the TMUA. TMUA-P1X-MM5-02 is set for a no-calculator target of about 180 seconds; the worked solution shows the fastest by-hand route.

Which TMUA specification point is TMUA-P1X-MM5-02?

TMUA-P1X-MM5-02 is Paper P1 · Exponentials and logarithms (specification code MM5), level 2. Drill more of the same topic from this page.

TMUA-P1X-MM5-02 — Paper P1 · Exponentials and logarithms · Level 2

P1MM5Level 2~180s target

Spec: MM5 · No calculator · ~180s

Solve

\log_2 x + \log_2(x + 2) = 3

, where

x

is real.

Options

$2$
$-4$
$2$ and $-4$
$4$
no solution

Letters only — the answer key is hidden. Work it out, then check the solution below.

Hint (check trope)

No written hint yet — check the trope: log-domain, extraneous-root. Name the trap first, work the stem by hand, then open the solution below.

Show solution

Combine:

\log_2(x(x + 2)) = 3

, so

x^2 + 2x - 8 = 0

giving

x = 2

x = -4

. But

x = -4

makes both original logs undefined, so only

x = 2

. Trap: “

2

and

-4

” keeps the extraneous root — plausible if you skip the domain check.

Keep practising

Same topic · same level
P1MM5Level 2
TMUA-P1-MM5-004
Solve 5^2x = 125.
Exponentials and logarithms
Open TMUA-P1-MM5-004 →
Same trap: log-domain
P1MM5Level 2
TMUA-P1-MM5-005
Solve _2 x + _2(x - 2) = 3, where x is real.
Exponentials and logarithms
Open TMUA-P1-MM5-005 →
Step up a level
P1MM5Level 3
TMUA-P1-MM5-009
What is the sum of all real solutions of 4^x - 3 · 2^x+1 + 8 = 0?
Exponentials and logarithms
Open TMUA-P1-MM5-009 →

Browse more

Loading…

Keep practising

Same topic · same level

P1MM5Level 2

TMUA-P1-MM5-004

Solve 5^2x = 125.

Exponentials and logarithms

Open TMUA-P1-MM5-004 →

Same trap: log-domain

P1MM5Level 2

TMUA-P1-MM5-005

Solve _2 x + _2(x - 2) = 3, where x is real.

Exponentials and logarithms

Open TMUA-P1-MM5-005 →

Step up a level

P1MM5Level 3

TMUA-P1-MM5-009

What is the sum of all real solutions of 4^x - 3 · 2^x+1 + 8 = 0?

Exponentials and logarithms

Open TMUA-P1-MM5-009 →

TMUA-P1X-MM5-02 — Paper P1 · Exponentials and logarithms · Level 2

Options

Keep practising

Master Exponentials and logarithms

TMUA-P1X-MM5-02 — Paper P1 · Exponentials and logarithms · Level 2

Options

Keep practising

Master Exponentials and logarithms