Logaritmus

1. Felt: x>`1/2`

`log_5(2x-1)` = 3

`5^3` = 125 = 2x - 1

x= 63

2. lg x = 4 -lg 2

Felt: x>0
lg x = lg 10000 -lg 2 = lg (10000/2)

x= 5000

3. x>1

lg (3x+1) - lg(x-1) = lg2 + lg 5

`(3x+1)/(x-1)` = 10

3x+1 = 10x-10

x= `11/7`

4.

Felt: x>4

lg (x+3) + lg (x-4) = lg(x+3) + lg5

Kivonhatunk mindkét oldalból (lg(x+3))-at.

lg (x-4) = lg 5

x-4 = 5

x=9

5. lg^2 (x) - 6 lg(x) + 8 = 0

Felt: x>0

lg(x)= a

a^2-6a+8 = 0

(a-2)(a-4)=0

`a_1`=2, `a_2`=4

lg(x)=2 -> `x_1`=100

lg(x)=6 -> `x_2`=10000

6. `log_3log_2log_3 (3x-2)` = 0

`log_2log_3 (3x-2)` =1

`log_3 (3x-2)` = 2

3x-2 = 9

x=`11/3`

7.
Felt: x>0

`log_2 x` + `2*log_4x` + `3*log_8x` = 3

`1/(log_x2)` + `2/log_x(2^2)` + `3/(log_x(2^3)` = `1/(log_x2)`+`1/(log_x2)`+`1/(log_x2)`= `3/(log_x2)` = 3

`log_x2` = 1

x=2