Maths(exponement Functions and Logarithmic Functions)

1. log4√a + loga2 / log√a

= loga1/4 + 2loga / loga1/2

= 1/4 loga + 2loga / (1/2) loga

= 1/4 loga + 4

2. log√24

= log241/2

= 1/2 log24

= 1/2 log(23 X 3)

= 1/2 (log23 + log3)

= 1/2 (3log2 + log3)

= 1/2 (3s + t)

3. log(3x - 1) + log(x - 1) = log7 + 1

log[(3x - 1)(x - 1)] = log7 + log10

log(3x2 – 4x + 1) = log(7 X 10)

log(3x2 – 4x + 1) = log70

→ 3x2 – 4x + 1 = 70

3x2 – 4x – 69 = 0

x = 5.51 (cor. to 3 sig. fig.) or -4.18 (rejected)

4. 3logx + log1/2x = log8

logx3 + logx/2 = log8

log(x3 X x/2) = log8

log(x4/2) = log8

→x4/2 = 8

x4 = 16

x = 2 or -2 (rejected)

1)
what is (log^4)開方a?
2)log開方24 = 1/2 log24 = 1/2(log 8+log 3)
= 1/2(3log2+t)
=1/2(3s+t)
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