Answer :
To solve the logarithmic equation log_5(6x+553)=4, transform it into its exponential form, simplify, and solve for x step by step to find that x = 12.
To solve the equation log_5(6x+553)=4, we can begin by eliminating the logarithm to solve for x. First, we rewrite the equation as an exponential equation because the logarithmic equation logb(A) = C is equivalent to the exponential equation bC = A. In our case, the base is 5, and it is raised to the power of 4.
Here are the step-by-step solutions:
- Rewrite the equation in its exponential form: 54 = 6x + 553.
- Calculate the power of 5: 54 is 625.
- Simplify the equation: 625 = 6x + 553.
- Subtract 553 from both sides to isolate the term with x: 625 - 553 = 6x.
- Simplify the subtraction to find the value: 72 = 6x.
- Finally, divide both sides by 6 to solve for x: 72 / 6 = x.
- The solution is x = 12.
Therefore, the missing part 6x+553 in the original equation should be followed by = 625 to continue the solution process, which eventually leads to x = 12.