# Photocopier

A photocopier enlarges a picture in the ratio 7:4. How many times will a picture of size 6cm by 4cm be enlarged to fit on a 30cm by 20 cm page?

Result

n =  2.876

#### Solution:

$a_{1}=6 \ \text{cm} \ \\ a_{2}=30 \ \text{cm} \ \\ k=7/4=\dfrac{ 7 }{ 4 }=1.75 \ \\ a_{2}=k^n \cdot \ a_{1} \ \\ a_{2}/a_{1}=k^n \ \\ n=\log(a_{2}/a_{1})/\log(k)=\log(30/6)/\log(1.75) \doteq 2.876$

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