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

Worked solution for TMUA-P1-MM5-009 is revealed on this page behind the solution details.

Why isn't the answer to TMUA-P1-MM5-009 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1-MM5-009 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1-MM5-009?

No — calculators are banned in the TMUA. TMUA-P1-MM5-009 is set for a no-calculator target of about 240 seconds; the worked solution shows the fastest by-hand route.

Which TMUA specification point is TMUA-P1-MM5-009?

TMUA-P1-MM5-009 is Paper P1 · Exponentials and logarithms (specification code MM5), level 3. Drill more of the same topic from this page.

TMUA-P1-MM5-009 — Paper P1 · Exponentials and logarithms · Level 3

P1MM5Level 3~240s target

Spec: MM5 · No calculator · ~240s

What is the sum of all real solutions of

4^x - 3 \cdot 2^{x+1} + 8 = 0

Options

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

Write everything in base

2

: with

y = 2^x

y^2 - 6y + 8 = 0

gives

y = 2

y = 4

, so

x = 1

x = 2

, whose sum is

3

. Trap:

6

is the sum of the

y

-values — plausible if you solve the quadratic but forget to convert back to

x

Keep practising

Same topic · same level
P1MM5Level 3
TMUA-P1-MM5-010
Solve _3(2x + 1) - _3(x - 1) = 2, where x is real.
Exponentials and logarithms
Open TMUA-P1-MM5-010 →
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 →
More in this topic
P1MM5Level 3
TMUA-P1-MM5-016
Solve _2 x + _2(x-2) = 3.
Exponentials and logarithms
Open TMUA-P1-MM5-016 →

Browse more

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Keep practising

Same topic · same level

P1MM5Level 3

TMUA-P1-MM5-010

Solve _3(2x + 1) - _3(x - 1) = 2, where x is real.

Exponentials and logarithms

Open TMUA-P1-MM5-010 →

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 →

TMUA-P1-MM5-009 — Paper P1 · Exponentials and logarithms · Level 3

Options

Keep practising

Master Exponentials and logarithms

TMUA-P1-MM5-009 — Paper P1 · Exponentials and logarithms · Level 3

Options

Keep practising

Master Exponentials and logarithms