F.4 Maths-Exponential Function

2009-11-08 9:02 pm
It is given that 5^x=0.5. If 5^-kx=8,find the value of k.

回答 (2)

2009-11-08 9:24 pm
✔ 最佳答案
5^-kx=8

(5^x)^(-k) = 8

0.5^(-k) = 8

[2^(-1)]^(-k) = 8

2^(-1 * -k) = 8

2^k = 8

2^k = 2^3

k = 3
2009-11-08 10:14 pm
X = log 0.5/log5 = -0.431; and

kX = log 8/log 5 = 1.292.


therefore, k = 1.292/-0.431 =-2.997
= -3 (round up to nearest integer);


(Proof 5^-0.431 = 0.5 and 5^1.292 = 8)


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