Given that _2 x = 5, what is the value of _2(x^3)?

Worked solution for TMUA-P1-MM5-007 is revealed on this page behind the solution details.

Why isn't the answer to TMUA-P1-MM5-007 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1-MM5-007 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1-MM5-007?

No — calculators are banned in the TMUA. TMUA-P1-MM5-007 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-MM5-007?

TMUA-P1-MM5-007 is Paper P1 · Exponentials and logarithms (specification code MM5), level 2. Drill more of the same topic from this page.

TMUA-P1-MM5-007 — Paper P1 · Exponentials and logarithms · Level 2

P1MM5Level 2~150s target

Spec: MM5 · No calculator · ~150s

Given that

\log_2 x = 5

, what is the value of

\log_2(x^3)

Options

$10$
$25$
$15$
$125$
$8$

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-power-law, power-placement. Name the trap first, work the stem by hand, then open the solution below.

Show solution

Power law:

\log_2(x^3) = 3\log_2 x = 3 \times 5 = 15

. Trap:

125

cubes the

5

— plausible if you confuse

\log(x^3)

with

(\log x)^3

Keep practising

Same topic · same level
P1MM5Level 2
TMUA-P1-MM5-004
Solve 5^2x = 125.
Exponentials and logarithms
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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?
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More in this topic
P1MM5Level 2
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Solve _2 x + _2(x - 2) = 3, where x is real.
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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 →

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-P1-MM5-007 — Paper P1 · Exponentials and logarithms · Level 2

Options

Keep practising

Master Exponentials and logarithms

TMUA-P1-MM5-007 — Paper P1 · Exponentials and logarithms · Level 2

Options

Keep practising

Master Exponentials and logarithms