Solve for x
log[1/3](x^(2) + x) - log[1/3] (x^(2) - x) = -1
Steps too please.
so far I tried this and I got 3 = (x+1) / (x-1)
I asked this question before, but what would x= ?
I solved it
great
To solve for x in the equation:
log[1/3](x^(2) + x) - log[1/3](x^(2) - x) = -1
Here are the steps to solve it:
Step 1: Use the formula for logarithmic subtraction:
log(base a)(x/y) = log(base a)x - log(base a)y
Applying this formula, the equation can be rewritten as:
log[1/3]((x^(2) + x)/(x^(2) - x)) = -1
Step 2: Use the definition of logarithm to rewrite the equation as an exponential equation:
1/3^(-1) = (x^(2) + x)/(x^(2) - x)
Step 3: Simplify the exponents:
3 = (x^(2) + x)/(x^(2) - x)
Step 4: Cross-multiply:
3(x^(2) - x) = x^(2) + x
Step 5: Expand and simplify:
3x^(2) - 3x = x^(2) + x
Step 6: Move all terms to one side to set the equation equal to zero:
3x^(2) - 3x - x^(2) - x = 0
2x^(2) - 4x = 0
Step 7: Factor out common terms:
2x(x - 2) = 0
Step 8: Apply the zero product property:
2x = 0 or x - 2 = 0
Step 9: Solve for x:
For 2x = 0:
x = 0
For x - 2 = 0:
x = 2
Hence, the solution is x = 0 or x = 2.