Paper 1 · indices / exponential equations

Solve the equation $5^{x-1} + 5^{x-2} = 30$ .

x = 2

x = 3

x = 5

x = 125

Explanation:

5^{x-1}+5^{x-2}=5^x\left(\tfrac15+\tfrac1{25}\right)=\tfrac{6}{25}5^x=30

, so

5^x=125=5^3

and

x=3

Derived from ZIMSEC Mathematics Paper 1, November 2013, Q1

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