2014 DSE Maths Paper 1 Q15

Let log8 y = Y , log4 x = X , the y-intercept = 1 since the x-intercept = 1 and the slope of the line is - 1/3.
By intercept form,
X/3 + Y/1 = 1
X + 3Y = 3
log4 x + 3log8 y = 3
(log x) / log 4 + (3log y) / log 8 = 3
(log x) / (2log 2) + (3log y) / (3log 2) = 3
3log x + 6log y = 18log 2
log x³ + log y⁶ = log 2¹⁸
log (x³ y⁶) = log 2¹⁸
x³ y⁶= 2¹⁸
y⁶ = 2¹⁸ x⁻³
y = 2³ x⁻³ˡ ⁶
y = 8x⁻¹ˡ ²∴ A = 8 , k = -1/2.

2015-02-17 20:16:47 補充：
the y-intercept = 1 since the x-intercept = 3 and the slope of the line is - 1/3.

2015-02-17 20:54:29 補充：
Method 2:

log₄x + 3log₈ y = 3
2^(log₄x + 3log₈ y) = 2^3
(2^log₄x) (2^3log₈ y) = 8
(4^log₄x^½) (8^log₈ y) = 8
(x^½) y = 8
y = 8x^ -½