## Question

secondary 3 | A Maths

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##### Sejwwkwkwleo

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I am unsure of how I'm supposed to do logarithms

Date Posted: 6 months ago
Views: 53
Snell
6 months ago
revise the laws of logarithm

(a)(i)
log₂ √x
= log₂ (x^½)
= ½ log₂ (x)
since log₂ x = p,
½ log₂ (x)
= ½ p

(ii)
log₂ xy²
= log₂ x + log₂ y²
= log₂ x + 2 log₂ y

since log₂ x = p, log₂ y = q,
log₂ x + 2 log₂ y
= p + 2q

(iii)
log₄ (4x/y)
= log₂ (4x/y) / log₂ 4
= [ log₂ 4x - log₂ y ] / log₂ 2²
= [ log₂ 4 + log₂ x - log₂ y ] / 2 log₂ 2

since log₂ x = p, log₂ y = q, & log₂ 2 = 1,
[ log₂ 4 + log₂ x - log₂ y ] / 2 log₂ 2
= [ log₂ 2² + p - q ] / 2
= [2 log₂ 2 + p - q ] / 2

since log₂ 2 = 1,
= [2 + p - q ] / 2
= 1 + ½(p - q)

(b)
lg x + lg[5(x+1) - 2 = 0

since lg 100 = 2,
lg x + lg[5(x+1) - lg 100 = 0
lg [ x (5x + 5)] - lg 100 = 0
lg (5x²+ 5x) - lg 100 = 0
lg [(5x²+ 5x)/100] = 0
lg [(x²+ x)/20] = 0

since lg 1 = 0,
lg [(x²+ x)/20] = lg 1
(x²+ x)/20 = 1
x²+ x = 20
x² + x - 20 = 0
(x + 5)(x - 4) = 0
x = -5 or x = 4

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