Question

Log1/6 (7x-9)=log1/6 (2x+6) помогите пожалуйста!

Answer 1

Log₁/₆ (7x-9)=log₁/₆ (2x+6)
ОДЗ:
7x-9>0   x>9/7       
2x+6>0  x>-3
7x-9=2x+6
5x=15
x=3

Answer 2

Solving the Equation log1/6(7x-9) = log1/6(2x+6)

To solve the equation log1/6(7x-9) = log1/6(2x+6), we can use the property of logarithms that states if loga(b) = loga(c), then b = c. In this case, we have log1/6(7x-9) = log1/6(2x+6), so we can set the arguments of the logarithms equal to each other and solve for x.

Step 1: Set the arguments of the logarithms equal to each other: log1/6(7x-9) = log1/6(2x+6)

Step 2: Solve for x: 7x - 9 = 2x + 6

Step 3: Simplify and solve for x: 7x - 2x = 6 + 9 5x = 15 x = 3

So, the solution to the equation log1/6(7x-9) = log1/6(2x+6) is x = 3.

(#1)

Conclusion

The solution to the equation log1/6(7x-9) = log1/6(2x+6) is x = 3.