Answer :
To solve the equation [tex]\(\log_x 3125 = 5\)[/tex], you can follow these steps:
1. Understand the Logarithm: The equation [tex]\(\log_x 3125 = 5\)[/tex] means that [tex]\(x^5 = 3125\)[/tex]. This tells us that the number [tex]\(x\)[/tex], raised to the power of 5, equals 3125.
2. Rewrite the Equation: We need to find the value of [tex]\(x\)[/tex] that satisfies this equation. So, we have the equation [tex]\(x^5 = 3125\)[/tex].
3. Solve for [tex]\(x\)[/tex]: To find [tex]\(x\)[/tex], we need to take the fifth root of 3125. In mathematical terms, [tex]\(x = 3125^{1/5}\)[/tex].
4. Calculate the Fifth Root: When you calculate the fifth root of 3125, you find that [tex]\(x\)[/tex] is approximately equal to 5.
So, the solution to the equation [tex]\(\log_x 3125 = 5\)[/tex] is [tex]\(x = 5\)[/tex].
1. Understand the Logarithm: The equation [tex]\(\log_x 3125 = 5\)[/tex] means that [tex]\(x^5 = 3125\)[/tex]. This tells us that the number [tex]\(x\)[/tex], raised to the power of 5, equals 3125.
2. Rewrite the Equation: We need to find the value of [tex]\(x\)[/tex] that satisfies this equation. So, we have the equation [tex]\(x^5 = 3125\)[/tex].
3. Solve for [tex]\(x\)[/tex]: To find [tex]\(x\)[/tex], we need to take the fifth root of 3125. In mathematical terms, [tex]\(x = 3125^{1/5}\)[/tex].
4. Calculate the Fifth Root: When you calculate the fifth root of 3125, you find that [tex]\(x\)[/tex] is approximately equal to 5.
So, the solution to the equation [tex]\(\log_x 3125 = 5\)[/tex] is [tex]\(x = 5\)[/tex].
