To solve the equation $4 - \log(7 - x) = 3$, let's go through the steps in detail.

Step-by-Step Solution

1. Isolate the logarithmic term: $4 - \log(7 - x) = 3$ Subtract 4 from both sides: $-\log(7 - x) = -1$ Multiply both sides by -1 to get: $\log(7 - x) = 1$

2. Rewrite the equation in exponential form: Since $\log(7 - x) = 1$, we can rewrite this as: $7 - x = 10^1$ Simplify the right side: $7 - x = 10$

3. Solve for $x$: Subtract 7 from both sides: $-x = 3$ Multiply by -1: $x = -3$

Solution

The solution is: $x = -3$

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Related Questions to Explore

1. How can logarithmic equations be solved when they have multiple logarithmic terms?
2. What steps are involved in converting logarithmic equations to exponential form?
3. How can we check for extraneous solutions in logarithmic equations?
4. How does the base of the logarithm affect the solution to a logarithmic equation?
5. How do we solve logarithmic equations that include constants on both sides?

Tip

When solving logarithmic equations, always check that the solution is within the domain of the logarithmic function (i.e., the argument must be positive).