Question

Need help with Logarithmic Question, heres pic

Answer 1

Answer: x = -5/28

Work Shown:

`\log_8(7)+\log_8(-4\text{x}) = \log_8(5)\\\\\log_8(7(-4\text{x})) = \log_8(5) \ \ \text{ ... see note1 below}\\\\\log_8(-28\text{x}) = \log_8(5)\\\\-28\text{x} = 5 \ \ \text{ ... see note2}\\\\\text{x} = -5/28\\\\`

• Note1: Use the log rule of log(A)+log(B) = log(A*B)
• Note2: If log(A) = log(B), then A = B. This is the "one-to-one property" that your teacher is referring to.