Log5 (1-x)=log5 (30)-log5 (2-x)

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To solve this logarithmic equation, we can use the property of logarithms that states:

log_a(b) - log_a(c) = log_a(b/c)

Substituting the given values into the equation, we have:

log5(1-x) = log5(30) - log5(2-x)

Using the above property, we can rewrite the right side of the equation as a single logarithm:

log5(1-x) = log5(30/2-x)

Now, we can simplify the right side:

log5(1-x) = log5(15-x)

Since the bases are the same, we can set the arguments of the logarithms equal to each other:

1-x = 15-x

Solving for x, we get:

1 = 15

This is a contradiction, so there are no solutions to the equation log5(1-x) = log5(30) - log5(2-x).