Exponential Equations (Edexcel A-Level Mathematics): Flashcards

Take logs of both sides of the equation.

Use the rule: $\log(a^b) = b \cdot \log(a)$.

$x = \log(2.8) / \log(5) \approx 0.640$ (to 3sf).

You can use either log or ln to solve.

$x = \log_2(7.2) - 3 \approx -1.17$ (to 2 decimal places).

Expand to $(x + 3) \log(2)$.

Use product, quotient, and power rules for simplification.

$x = (2\log(3) + 4\log(5) - 3\log(2)) / (\log(2) + \log(5))$.

It equals $c \cdot \log_a(b)$.

Combine: $\log(x^3) = 4$, $x^3 = 10^4$, $x = 10^{4/3}$.