### Home > CCA2 > Chapter 6 > Lesson 6.2.2 > Problem6-113

6-113.

Solve each of the following equations to the nearest 0.001. Homework Help ✎

1. $(5.825)^{(x−3)}=120$

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

Apply the Power Property:

Divide both sides of the equation by log(5.825):

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

log(5.825)(x − 3) = log(120)

(x − 3)log(5.825) = log(120)

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

2. $18(1.2)^{(2x−1)}=900$

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