Given:
The given expression is
![log_2{18}=x-1](https://img.qammunity.org/2021/formulas/mathematics/college/xbloiatwswjvp3b5lhphtst40sjxoeklpe.png)
We need to determine the equivalent expression.
Equivalent expression:
The equivalent expression of the given expression can be determined using the property.
If
then it is equivalent to
![x=b^y](https://img.qammunity.org/2021/formulas/mathematics/college/1v67o42kkrqvmj35xtu5i1e6mrftmfk4k0.png)
The given expression is of the form
, where
and
![y=x-1](https://img.qammunity.org/2021/formulas/mathematics/high-school/ppmeebbmc50z1o7iz4pyhsd4759fddznbn.png)
Thus using the above property, the given expression can be written as,
![18=2^(x-1)](https://img.qammunity.org/2021/formulas/mathematics/college/6z3bjaxodw25bu8ax6x4y8fawygkcr1kno.png)
Thus, the equivalent expression is
![18=2^(x-1)](https://img.qammunity.org/2021/formulas/mathematics/college/6z3bjaxodw25bu8ax6x4y8fawygkcr1kno.png)
Hence, Option d is the correct answer.