F.4 Maths logarithm&indice40

yuet

2010-01-08 3:30 am

15) Given that 8^(5+2x) = 4^(2+5x) , Find x
Ans: 4
26) If log a = 0.3456, then log 1/a=
Ans: 1.6544
33) 8^(log_2 3) equals
Ans: 27
38) If 2log x + log y= 3 and 3log x - log y= 7, then x, y equal respectively
Ans : 100, 0.1
39) Find the no. whose logarithm is 3.1355
Ans : 0.001366
40) Solve for x, given that (log x)62 - 2log x -3 =0
Ans: 1/10000 or 10
** the ans given may be wrong, pls ans with steps; if there is no steps, can you
please explain how to calculate to me?
THX a LOT!!!!

回答 (1)

用戶9112

2010-01-08 4:07 am

✔ 最佳答案

15) 8^(5+2x) = 4^(2+5x)
(2^3)^(5+2x) = (2^2)^(2+5x)
2^(15+6x) = 2^(4+10x)
15+6x = 4+10x
11=4x
x = 11/4
26) If log a = 0.3456,
then log 1/a = log1 - loga
= 0 - 0.3456
= -0.3456
33) 8^(log_2 3)
= 8^(log3/log2)
= 8^(log3/log8 * log8/log2)
= 8^(log3/log8 * log2^3/log2)
= 8^(log3/log8 * 3)
= [8^(log_8 3)]^3
= 3^3
= 27
38) 2log x + log y = 3... (1)
3log x - log y = 7 ... (2)
5log x = 10
log x = 2
x = 100
Sub into (1), 2log 100 + log y = 3
4 + log y = 3
log y = -1
y = 0.1
39) Find the no. whose logarithm is 3.1355
log x = 3.1355
x = 10^(3.1355)
x = 1366
Alternatively since log1.366 = 0.1355
3 + log1.366 = 3.1355
log1000 + log1.366 = 3.1355
log1366 = 3.1355
40) (log x)^2 - 2log x -3 =0
Let u = log x
u^2 - 2u - 3 = 0
(u - 3)(u + 1) = 0
u = 3 or u = -1
log x = 3 or log x = -1
x = 1000 or x = 0.1

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