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

Worked solution for TMUA-P1-MM5-017 is revealed on this page behind the solution details.

Why isn't the answer to TMUA-P1-MM5-017 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1-MM5-017 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1-MM5-017?

No — calculators are banned in the TMUA. TMUA-P1-MM5-017 is set for a no-calculator target of about 150 seconds; the worked solution shows the fastest by-hand route.

Which TMUA specification point is TMUA-P1-MM5-017?

TMUA-P1-MM5-017 is Paper P1 · Exponentials and logarithms (specification code MM5), level 3. Drill more of the same topic from this page.

TMUA-P1-MM5-017 — Paper P1 · Exponentials and logarithms · Level 3

P1MM5Level 3~150s target

Spec: MM5 · No calculator · ~150s

Find the sum of all solutions of

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

Options

$0$
$1$
$\frac{4}{3}$
$2$

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: exponential-quadratics, hidden-quadratic. Name the trap first, work the stem by hand, then open the solution below.

Show solution

Let

y = 3^x

y^2 - 4y + 3 = (y-1)(y-3) = 0

, so

3^x = 1

3

giving

x = 0

x = 1

with sum

1

, so the correct is B. Trap:

0

reports only the smaller solution instead of the sum.

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Keep practising

Same topic · same 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-P1-MM5-017 — Paper P1 · Exponentials and logarithms · Level 3

Options

Keep practising

Master Exponentials and logarithms

TMUA-P1-MM5-017 — Paper P1 · Exponentials and logarithms · Level 3

Options

Keep practising

Master Exponentials and logarithms