Find all real solutions of 3^2x - 4 · 3^x + 3 = 0.

Worked solution for TMUA-P1X-MM5-03 is revealed on this page behind the solution details.

Why isn't the answer to TMUA-P1X-MM5-03 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1X-MM5-03 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1X-MM5-03?

No — calculators are banned in the TMUA. TMUA-P1X-MM5-03 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-MM5-03?

TMUA-P1X-MM5-03 is Paper P1 · Exponentials and logarithms (specification code MM5), level 2. Drill more of the same topic from this page.

TMUA-P1X-MM5-03 — Paper P1 · Exponentials and logarithms · Level 2

P1MM5Level 2~180s target

Spec: MM5 · No calculator · ~180s

Find all real solutions of

3^{2x} - 4 \cdot 3^x + 3 = 0

Options

$1$ and $3$
$0$ only
$0$ and $1$
$1$ only
$3$ only

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: quadratic-in-exp, y-vs-x-trap. Name the trap first, work the stem by hand, then open the solution below.

Show solution

Set

y = 3^x

y^2 - 4y + 3 = 0

gives

y = 1

y = 3

, so

3^x = 1

3

and

x = 0

x = 1

. Trap:

1

and

3

reports the values of

y

, not

x

— plausible if you stop after factorising.

Keep practising

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Open TMUA-P1-MM5-004 →
Same trap: quadratic-in-exp
P1MM5Level 2
TMUA-P1-MM5-006
Find all real solutions of 2^2x - 5 · 2^x + 4 = 0.
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Open TMUA-P1-MM5-006 →
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

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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: quadratic-in-exp

P1MM5Level 2

TMUA-P1-MM5-006

Find all real solutions of 2^2x - 5 · 2^x + 4 = 0.

Exponentials and logarithms

Open TMUA-P1-MM5-006 →

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-MM5-03 — Paper P1 · Exponentials and logarithms · Level 2

Options

Keep practising

Master Exponentials and logarithms

TMUA-P1X-MM5-03 — Paper P1 · Exponentials and logarithms · Level 2

Options

Keep practising

Master Exponentials and logarithms