Solve for x log of x-4=3

Problem

(log_)(x−4)=3

Solution

1. Identify the base of the logarithm. Since no base is specified, it is assumed to be the common logarithm with base 10

(log_10)(x−4)=3

2. Rewrite the logarithmic equation in its equivalent exponential form using the definition (log_b)(y)=a⇔ba=y

10=x−4

3. Evaluate the power of 10 on the left side of the equation.

1000=x−4

4. Isolate the variable x by adding 4 to both sides of the equation.

1000+4=x

x=1004

5. Verify that the solution is within the domain of the original logarithmic function. Since 1004 - 4 = 1000,w*h*i*c*h*i*s(g)*r*e*a*t*e*r*t*h*a*n$, the solution is valid.

Final Answer

(log_)(x−4)=3⇒x=1004

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