Question

Logстепень внизу1/4(x-3)=-1

Answer 1

Log₁/₄(x-3)=-1           ОДЗ: x-3>0   x>3.
x-3=(1/4)⁻¹
x-3=4
x=7.
Ответ: x=7.

Answer 2

To solve the logarithmic equation, you'll need to isolate the logarithmic term and then apply the properties of logarithms to solve for 'x'. The given equation is:

log₁/₄(x - 3) = -1

Step 1: Convert the equation to exponential form using the definition of logarithms. In general, if logₐ(b) = c, then aᶜ = b.

In this case: log₁/₄(x - 3) = -1 ---> ₁/₄⁻¹ = x - 3

Step 2: Simplify the right-hand side.

₁/₄⁻¹ = 4 So, the equation becomes: 4 = x - 3

Step 3: Isolate 'x' by bringing the constant term to the other side.

x = 4 + 3

Step 4: Perform the addition to find the value of 'x'.

x = 7

Therefore, the solution to the equation is x = 7.