logarithmic functions 2條(f4)

23.
(b)
log16 x = log2 x + 3
log16 x = (log x / log 2) + 3
log16 x = ( 4 log x / 4 log 2) + 3
log16 x = ( 4 log x / log 16) + 3
log16 x = 4 log16 x + 3
- 3 log16 x = 3
log16 x = -1
x = 16⁻¹
x = 1/16


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26.
Let $y be the price of the fresh shrimp per 100 g yesterday.
N in yesterday = 74 - 50 log y

Today :
(74 - 50 log y) - 7 = 74 - 50 log (y + 5)
-50 log y - 7 = -50 log (y + 5)
50 [log (y + 5) - log y] = 7
log [(y + 5)/y] = 0.14
(y + 5)/y = 10^0.14
y + 5 = (10^0.14)y
y(10^0.14 - 1) = 5
y = 5/(10^0.14 - 1)
y = 13

The price of fresh shrimp per 100 g yesterday = $13