Solve each of the following equations to the nearest $0.001$.

1. $(5.825)^{(x−3)}=120$ 

   Step 1(a):

   Since you are solving for an exponent, take the log of each side: 

   $\text{log}(5.825)^{(x − 3)} = \text{log}(120)$

   Step 2(a):

   Apply the Power Property:

   $(x − 3)\text{log}(5.825)= \text{log}(120)$

   Step 3(a):

   Divide both sides of the equation by $\text{log}\left(5.825\right)$:

   $\frac{(x-3) \text{log}(5.825)}{ \text{log}(5.825)} = \frac{ \log (120)}{ \log (5.825)}$

   Step 4(a):

   Add $3$ to both sides and use your calculator.
   Remember to round to the nearest $0.001$.

2. $18(1.2)^{(2x−1)}=900$ 

   Hint (b):

   Divide both sides of the equation by $18$.
   See part (a).