Question 42

x = b^5

To find the value of x in terms of b, we can rearrange the equation 58 + 2 * logb(x) = 68. By isolating logb(x) and converting back from logarithmic form, we find that x equals b raised to the power of 5.

A) 5/b

This option suggests that x is inversely proportional to b, which does not align with the logarithmic relationship defined in the equation. The logarithmic transformation does not yield a fraction in this case, making this choice incorrect.

B) 5b

This answer implies that x is directly proportional to b, but it does not follow the logarithmic properties indicated in the equation. The equation leads to an exponential relationship, not a linear one, thus ruling out this option.

C) 5^b

This option indicates that x is based on 5 raised to the power of b. However, the equation specifically involves b as the base in the logarithm, which does not support this formulation. The correct transformation does not yield this result.

D) b^5

This choice correctly follows the transformations applied to the original logarithmic equation. By rearranging 58 + 2 * logb(x) = 68, we arrive at logb(x) = 5, which directly translates to x = b^5 when converted from logarithmic to exponential form.

E) b^10

This option suggests that x is equal to b raised to the power of 10. However, based on the logarithmic equation provided, the correct exponent derived from the calculations is 5, making this option incorrect.

Conclusion

The correct answer, x = b^5, accurately reflects the transformations applied to the logarithmic equation. All other options fail to represent the relationship established by the logarithm, either misinterpreting the base or the exponent, thereby confirming that D is the only valid solution.