Sketching Exponential Graphs

Edexcel IAL WMA12/01/P2/Jan 2020/Q9 (Exponentials &​​ Logarithms)

• Sketch the curve with equation​​ 

y = 3 × 4x

showing the coordinates of any points of intersection with the coordinate axes.​​ 

(2)​​ 

The curve with equation y = 61–x​​ meets the curve with equation​​ y=3×4x​​ at the point P.​​ 

• Show that the x coordinate of​​ P is​​ log10⁡2log10⁡24

(5)

SOLUTION

a- The y-intercept of​​ y = 3 × 4x​​ will be​​ 

y = 3 × 4x

y=3×40

y=3×1

y=3

b- ​​ Equating both curves’ equation to foind the cordinates of the point of intersection.​​ 

y=61-x1

y=3 x 4x2

61-x=3 x4x

66x=3 x 4x

6=3 x4xx6x

2=4x x6x

2=24x

Taking log on both sides​​ 

log10⁡2=log10⁡24x

log10⁡2=xlog10⁡24

log10⁡2log10⁡24 =x

x=log10⁡2log10⁡24

ALTERNATE METHOD

y=61-x1

y=3 x 4x2

61-x=3 x4x

Taking log on both sides​​ 

log10⁡61-x=log10⁡3 x 4x

1-xlog10⁡6=log10⁡3+xlog10⁡4

log10⁡6-xlog10⁡6=log10⁡3+xlog10⁡4

log10⁡6-log10⁡3=xlog10⁡4+xlog10⁡6

log10⁡2=xlog10⁡24

log10⁡2log10⁡24=x

x=log10⁡2log10⁡24