To solve the equation log(3x-1)-log(3x+1)=log16, we can combine the logarithmic terms using the quotient rule of logarithms, which states that log(a)-log(b) = log(a/b). Applying this rule, we get:
log((3x-1)/(3x+1)) = log16
Now we can eliminate the logarithm by exponentiating both sides with base 10, which gives:
(3x-1)/(3x+1) = 16
Next, we can cross-multiply and simplify as follows:
3x-1 = 16(3x+1)
3x-1 = 48x+16
-45x = 17
x = -17/45
Therefore, the solution to the equation log(3x-1)-log(3x+1)=log16 is x = -17/45. Note that this solution is valid only if 3x-1 and 3x+1 are both positive (since logarithms are defined only for positive arguments). Checking these conditions, we see that -1/3 < x < 1, so the solution is valid.
State the univers and solve each of the following equation
log(3x-1)-log(3x+1)=log16
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