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20 Days to Go(-11 Days): Logarithmic Transformation (下)

April 6, 2018
20 Days to Go(-11 Days): Logarithmic Transformation (下)
.font-size-custom{ font-size: 18px; line-height: 28px; } The figure below shows the graph of y = abx , where a and b are constants. Which of the following graphs represent the relation between xand log4? ?
20 Days to Go(-11 Days): Logarithmic Transformation (下)
20 Days to Go(-11 Days): Logarithmic Transformation (下)

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20 Days to Go(-11 Days): Logarithmic Transformation (下)
首先,用(0,3)代入y=abx
a=3
然後因為graph不斷下降, 可以推斷0
.font-size-custom{ font-size: 18px; line-height: 28px; } (可以用計數機試 , e.g. (0.5)2 , (0.5)5 , (0.5)10來觀察x愈大y愈小)
.font-size-custom{ font-size: 18px; line-height: 28px; } 要將y=abx轉變為一條有關x和log4y的equation
.font-size-custom{ font-size: 18px; line-height: 28px; } y=abx
.font-size-custom{ font-size: 18px; line-height: 28px; } log4y=log4abx
.font-size-custom{ font-size: 18px; line-height: 28px; } log4y=log4bx+ log4a
.font-size-custom{ font-size: 18px; line-height: 28px; } log4y=(log4b)x+log4a
.font-size-custom{ font-size: 18px; line-height: 28px; } 所以slope= log4b , y-intercept= log4a
.font-size-custom{ font-size: 18px; line-height: 28px; } 然後要留意slope究竟是正還是負數
.font-size-custom{ font-size: 18px; line-height: 28px; } log4b<0 ,因為0<b<1
.font-size-custom{ font-size: 18px; line-height: 28px; } y-intercept是正還是負數
.font-size-custom{ font-size: 18px; line-height: 28px; } log43>0
.font-size-custom{ font-size: 18px; line-height: 28px; } 所以這題slope是負數 , y-intercept是正數
.font-size-custom{ font-size: 18px; line-height: 28px; } 你就可以判定哪一張圖是正確答案 (A)
20 Days to Go(-11 Days): Logarithmic Transformation (下)
有同學將graph拉直去找答案 ,

但當0<a<1 , y-intercept會變成負數

所以有機會做錯
20 Days to Go(-11 Days): Logarithmic Transformation (下)

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