Exponential Equations (AQA A-Level Mathematics): Flashcards

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Exponential Equations
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Method to solve exponential eq. like 5x=2.85^x = 2.8

Take logs of both sides

Log rule: log⁡(ab)=?\log(a^b) = ?

blog⁡(a)b\log(a)

Can you use ln instead of log for exponential eq.?

Yes, same result

Method to solve log⁡a(x)=k\log_a(x) = k

Raise aa to both sides: x=akx = a^k

Simplify: alog⁡a(x)a^{\log_a(x)}

xx

Simplify: log⁡a(ax)\log_a(a^x)

xx

Does 101+102=10310^1 + 10^2 = 10^3?

No, can't distribute power over addition

Before raising base to power, ensure what?

Single term on each side

Why is x=−1x = -1 invalid in log⁡(x)=...\log(x) = ...?

Logs of negatives don't exist

Solve 5x=2.85^x = 2.8 (3sf)

x=log⁡(2.8)log⁡(5)≈0.640x = \frac{\log(2.8)}{\log(5)} \approx 0.640

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