有关log的问题： 各位帮帮忙！

ting_006

有关log的问题：
各位帮帮忙！

1.logarithm of 28 with respect to base x=4
what is the value of x??
ans:2.3

2.(5 to the power of x+1)(2 to the power of x+2)=(3 to the power of x+3)
Find the value of x.
ans:0.25

3.Solve the following question.
a. Logarithm of (2x to the power of 2)-5 with respect to base 3=2+logarithm of (x-1) with respect to base 3
ans:4

b. logarithm of x to the power of 3 with respect to base 8=(logarithm of 8 to the power of 3 with respect to base x)+8
ans:1/2,512

ivangile

1. logx 28 = 4
    logx 28 = logx x^4
    28=x^4
    x = 2.3

ting_006

回复 2# ivangile


是这样的啊？？

peaceboy

回复 3# ting_006
一群死高手不要来帮忙

   .(5 to the power of x+1)(2 to the power of x+2)=(3 to the power of x+3)
Find the value of x.

5^(x+1) 2^(x+2) = 3^x+3
5(5^x) 4(2^x) = 27(3^x)
20(10^x) = 27(3^x)
(10/3)^x = 27/20
x log  (10/3) = log 27/20
x= log (27/20) /l og  (10/3)
then use calculator


ans:0.25

3.Solve the following question.
a. Logarithm of (2x to the power of 2)-5 with respect to base 3=2+logarithm of (x-1) with respect to base 3
log3 (2x^2 - 5) = 2+ log3 (x-1)
log3 (2x^2 - 5) - log3 (x-1) = 2
log3 (2x^2 - 5)/(x-1) = 2
(2x^2 - 5)/(x-1) = 3^2 = 9
2x^2 - 5= 9x-9
2x^2 -9x+4 =0
(2x-1)(x-4)=0
x= 1/2 , 4

ans:4

b. logarithm of x to the power of 3 with respect to base 8=(logarithm of 8 to the power of 3 with respect to base x)+8


log8 x^3 = logx 8^3 + 8
               = 3 logx 8 +8
               = 3/log8 x + 8
3 log8 x - 3 /log8 x =8
let log8 x = a
3a- 3/a = 8
3a^2 -3 =8a
3a^2 - 8a - 3 =0
(3a+1)(a-3)=0
a= - 1/3 , 3
log8 x = -1/3 , 3
x = 8^(-1/3) , 3
x= 1/8^(1/3)  , 8^3
  = 1/2 , 512
ans:1/2,512

ting_006

回复 4# peaceboy

嘻嘻！！！
谢谢你的帮忙！！！！
真的很感谢哦~~
kangsahaimida!!!

ting_006

4.a)Find the least integral value of x such that (0.7)to the power of x+3 <0.01
Ans:10

b)Find the values of x that satisfy the inequality :
        3 to the power of 2x -10(3 to the power of 3x)+9 is less than and equal to 9
ans:0 less than or equal to x less than or equal to 2

Log

回复 6# ting_006
4.a)Find the least integral value of x such that (0.7)to the power of x+3 <0.01
Ans:10

b)Find the values of x that satisfy the inequality :
        3 to the power of 2x -10(3 to the power of 3x)+9 is less than and equal to 9
ans:0 less than or equal to x less than or equal to 2

4
a.  0.7^(x+3) < 0.01
     (0.7^x )(0.7^3) < 0.01
     (0.7^x) < 0.01/(0.7^3)
      (0.7^x)< 10/343
    log (0.7^x) <  log (10/343)
x  log 0.7 < log (10/343)
             x > log (10/343) / log 0.7   
             x > 9.9114
             integral value of x = 10 ,11.12,.....
   so the least integral value of x is 10.

  b.      3^(2x)-10(3^3x) + 9 ≤ 9   .....this inequality..??

nkrealman

回复  ting_006
4.a)Find the least integral value of x such that (0.7)to the power of x+3  log (10/ ...
Log 发表于 23-6-2011 12:16 AM

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