Final answer:
To determine x, rewrite the equation in exponential form. 7^3 = 3x + 43. Solve for x by isolating it on one side of the equation. The value of x is 100.
Step-by-step explanation:
To determine the value of x which satisfies the given equation, we can start by rewriting the equation in exponential form. Since log base 7 is used, the exponential form is 7 raised to the power of 3 equals 3x + 43.
7^3 = 3x + 43
343 = 3x + 43
Subtract 43 from both sides:
343 - 43 = 3x
300 = 3x
Divide both sides by 3 to isolate x:
x = 100
Therefore, the value of x that satisfies the equation is 100. Hence, the correct option is e) 100.