Solve for x log of 1-x = log of 10

Problem

(log_)(1−x)=(log_)(10)

Solution

1. Identify the logarithmic equation. Since both sides of the equation consist of a single logarithm with the same base, you can use the property of equality for logarithmic functions.

2. Apply the property that if (log_)(a)=(log_)(b) then a=b Set the arguments of the logarithms equal to each other.

1−x=10

3. Isolate the variable x by subtracting 1 from both sides of the equation.

−x=9

4. Solve for x by multiplying or dividing both sides by −1

x=−9

5. Check the solution by substituting x=−9 back into the original logarithmic expression to ensure the argument is positive. Since $1 - (-9) = 10,a*n*d0 > 0$, the solution is valid.

Final Answer

(log_)(1−x)=(log_)(10)⇒x=−9

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