Final answer:
To solve the logarithmic expression log₄(x+3)=-3, we convert it to its exponential form and solve for x, resulting in x being -191/64.
Step-by-step explanation:
The given logarithmic expression is log₄(x+3)=-3. To solve for x, we will use the knowledge that the logarithm function is the inverse function to the exponential function. This means that if log₄(y)=z, then 4⁺⁽=y.
To find the value of x, we need to rewrite the equation in its exponential form:
- 4⁺³ = x + 3
- (1/64) = x + 3
- x = (1/64) -3
- x = -3 + 1/64
- x = -191/64
Thus, the value of x would be -191/64 to satisfy the original logarithmic expression.