CAIE IGCSE Additional Math 6.3 Solve Exponential Equations Questions

Practise Cambridge IGCSE Additional Mathematics by solving exponential equations, rewriting bases and giving suitably accurate answers.

Exam points

Solve exponential equations by rewriting bases and equating exponents.
Use logarithms to solve equations with unlike bases and report suitable accuracy.
Check exponential substitutions and state the valid solution.

[Maximum number: 4]

Solve the equation $\mathrm{e}^{x^{2}-3}=25 \mathrm{e}^{7-x^{2}}$ .

$\mathrm{e}^{x^{2}-3-\left(7-x^{2}\right)}=25$ oe
Arrange as equation with one power of e

$2 x^{2}-10=\ln 25$ $x^{2}=\frac{\ln 25+10}{2}$ $x= \pm \sqrt{\frac{\ln 25+10}{2}}$ oe or $\pm \sqrt{\ln 5+5}$
isw

All question bank results loaded

CAIE IGCSE Additional Math 6.3 Solve Exponential Equations Questions question 1