Question

Solve each logarithmic equation algebraically. 3. log_(4)(5x+1)=log_(4)(8x-17)

Answer 1

To solve the equation log_4(5x+1) = log_4(8x-17), we equate the arguments and solve for x, obtaining the solution x = 6.

Step-by-step explanation:

To solve the logarithmic equation log_4(5x+1) = log_4(8x-17) algebraically, we start by applying the property that if two logarithms with the same base are equal, then their arguments must be equal. This gives us the equation 5x + 1 = 8x - 17.

Proceed with the following steps:

1. Subtract 5x from both sides: 1 = 3x - 17.
2. Add 17 to both sides: 18 = 3x.
3. Divide both sides by 3: x = 6.

Thus, the solution to the equation is x = 6.