SOLUTION: I have a question about the logarithmic equations. I'll use log[a, b] where a is the base of the logarithm. Is log[sqrt3,(1-x)^2] - log[sqrt3, (3-x)] < 2 equal to 2 *

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Question 996322: I have a question about the logarithmic equations. I'll use log[a, b] where a is the base of the logarithm.

Is
log[sqrt3,(1-x)^2] - log[sqrt3, (3-x)] < 2
equal to
2 * log[sqrt3, (1-x)] - log [sqrt3, (3-x)]<2
If they're not equal, why aren't they? Isn't the logarithm property of exponent is log(1-x)^2 = 2 * log(1-x)?
Found 2 solutions by MathLover1, rothauserc:
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!



...........change to base



....if log same, then
......solve for



.....use quadratic formula




exact solutions:




Answer by rothauserc(4718)   (Show Source): You can put this solution on YOUR website!
use the division logarithm rule
log[sqrt3,(1-x)^2] - log[sqrt3, (3-x)] = log[sqrt3, (1-x)^2 / (3-x)], therefore
log[sqrt3, (1-x)^2 / (3-x)] < 2
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