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18.03.2013

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log69, , log62 = k.

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, log69 = log632 = 2log63 = 2log66/2 = 2(log66 - log62) = 2(1 - k).

: 2(1 - k).


lg(x + 1.5) = -lgx.

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lg(x + 1.5) + lgx = 0. lgx(x + 1.5) = 0, . :

: x = ½.

: x = ½.


log2(9 - 2x)/(3 - x) = 1.
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, x ≠ 3 :

log2(9 - 2x) = 3 - x; :

9 - 2x = 23 - x;

2x + 8/2x - 9 = 0;

(2x)2 - 92x + 8 = 0; :

2x = 1 2x = 8. .. x = 0 x = 3. x = 3 ( ), : x = 0.

: x = 0.


log5(x - 2) + log5(x3 - 2) + log0.2(x - 2) = 4.

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, x > 2 (). , 5:

log5(x - 2) + 2log5(x3 - 2) - log5(x - 2) = 4.

2log5(x3 - 2) = 4.

log5(x3 - 2) = log525.

x3 - 2 = 25.

x3 = 27.

x = 3. .

: x = 3.


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