Final answer:
The solution to the logarithmic equation log₁/₂(x+5) = -3 is x = -39/8. This is found by converting the log equation to exponential form and then solving for x.
Step-by-step explanation:
To solve the logarithmic equation log₁/₂(x+5) = -3, we can use the definition of a logarithm. The equation can be rewritten in exponential form as 2 to the power of -3 equals x+5. This gives us:
2-3 = x + 5
Since 2-3 equals 1/23, which is 1/8, the equation simplifies to:
1/8 = x + 5
To find the value of x, we subtract 5 from both sides:
x = 1/8 - 5
x = 1/8 - 40/8
x = -39/8
Therefore, the solution to the equation is x = -39/8.