If b > 1 and 58 + 2 * logb(x) = 68 what is the value of x in terms of b?

Rationale

x = b^5.

To solve for x in the equation 58 + 2 * logb(x) = 68, we first isolate the logarithmic term, leading us to determine that x can be expressed as b raised to the power of 5.

A (5/b) YOUR ANSWER

This choice suggests that x is a fraction involving b. However, upon isolating the logarithmic term and solving for x, we find that it cannot be expressed as a fraction of 5 and b. Thus, this option does not satisfy the equation.

B (5b) YOUR ANSWER

This option implies that x is directly proportional to both 5 and b. However, substituting 5b into the original equation does not yield a solution consistent with the logarithmic properties and the base b, therefore it is incorrect.

C (5^b) YOUR ANSWER

This choice suggests that x is equal to 5 raised to the power of b. While it is a valid expression, it does not satisfy the logarithmic equation derived from the original problem since it does not relate to the base b in the logarithmic context.

D (b^5) CORRECT

This choice is correct as it directly arises from solving the logarithmic equation. By isolating the logarithm and exponentiating both sides, we derive that x must equal b raised to the power of 5.

E (b^10) YOUR ANSWER

This option implies that x is b raised to the power of 10. However, this does not align with the logarithmic equation derived earlier, leading to a discrepancy in the values and making it an incorrect choice.

Conclusion

Through the process of isolating the logarithmic term and applying properties of exponents, we find that x must equal b raised to the power of 5. This solution reflects the relationship defined by the logarithm in the equation, confirming that the only valid expression for x in terms of b is indeed b^5.

If b > 1 and 58 + 2 * logb(x) = 68 what is the value of x in terms of b?

x = b^5.

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