log4(little four) (40 - 3x) = 0
now i need to solve for x...
To solve the equation log4(40 - 3x) = 0 for x, we can follow these steps:
Step 1: Understand log4 notation
The equation log4(40 - 3x) = 0 represents a logarithmic equation with a base of 4. The logarithmic function is the inverse of the exponential function. In this case, log4(x) returns the exponent to which 4 must be raised to produce x.
Step 2: Apply the exponential form of logarithms
Since the logarithmic equation is in the form logb(x) = y, we can rewrite it in exponential form as b^y = x. In our case, we have log4(40 - 3x) = 0, so we can rewrite it as 4^0 = 40 - 3x.
Step 3: Simplify the equation
We know that any number raised to the power of 0 is equal to 1. Applying this rule, we have 1 = 40 - 3x.
Step 4: Isolate the variable
To solve for x, we need to isolate it on one side of the equation. Let's rearrange the equation: 1 - 40 = -3x.
Step 5: Solve for x
Combine like terms: -39 = -3x. Now, divide both sides of the equation by -3: x = -39/-3.
Step 6: Simplify the result
Dividing -39 by -3, we get x = 13.
Therefore, the solution to the equation log4(40 - 3x) = 0 is x = 13.