Solve. Where appropriate, include approximations to the nearest thousandth. If no solution exists, state this.
log[5] (5x - 1) = 1
5^1 = 5 = 5x -1
5x = 6
x = 1.200 (exactly)
To solve the equation log[5] (5x - 1) = 1, you need to rewrite it in exponential form. In exponential form, the equation becomes:
5^1 = 5x - 1
Simplifying the left side, we have:
5 = 5x - 1
To isolate the variable, we add 1 to both sides:
5 + 1 = 5x - 1 + 1
6 = 5x
Finally, we divide both sides by 5:
6/5 = 5x/5
x = 6/5
Therefore, the solution to the equation log[5] (5x - 1) = 1 is x = 6/5, or approximately 1.200 to the nearest thousandth.
To solve the equation log[5] (5x - 1) = 1, we need to isolate the variable x.
First, we'll rewrite the equation in exponential form. The logarithmic equation log[5] (5x - 1) = 1 is equivalent to saying that 5 raised to the power of 1 gives us 5x - 1:
5^1 = 5x - 1
Simplifying, we have:
5 = 5x - 1
Next, we'll bring the constant term to the opposite side of the equation:
5 + 1 = 5x
Simplifying further:
6 = 5x
Finally, we'll isolate x by dividing both sides of the equation by 5:
6/5 = x
Therefore, the solution to the equation log[5] (5x - 1) = 1 is x ≈ 1.200.