### Home > A2C > Chapter 7 > Lesson 7.2.2 > Problem7-111

7-111.

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

1. $(5.825)^{(x−3)}=120$

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

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

Apply the Power Property:

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

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

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

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

2. $18(1.2)^{(2x−1)}=900$

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