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Paper 1 · June 2013 · Logarithms and Exponentials

Solve the simultaneous equations $2^x + 3^y = 5$ and $2^{x+2} - 3^{y+1} = 13$ .

A

x = 0

,

y = 2

B

x = 4

,

y = 1

C

x = 1

,

y = 2

D

x = 2

,

y = 0

Explanation

With

p=2^x

and

q=3^y

:

p+q=5

and

4p-3q=13

. Solving gives

p=4

,

q=1

, so

2^x=4

(

x=2

) and

3^y=1

(

y=0

).

Derived from ZIMSEC Mathematics Paper 1, June 2013, Q1

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