CPM Homework Help : PC Problem 6-103

6-103.

Solve each of the following equations. Homework Help ✎
1. log₃(x + 9) − log₃ x + log₅ 25 = 4
2. 500(1.15)²^x⁻¹ + 1000 = 10000

Step 1(a):

log₃(x + 9) − log₃x + log₅5² = 4

Step 2(a):

log₃(x + 9) − log₃x + 2 = 4

Step 3(a):

log₃(x + 9) − log₃x = 2

Step 4(a):

$\text{log}_{3}\frac{x+9}{x}=2$

Step 5(a):

$3^{\text{log}_{3}\frac{x+9}{x}}=3^{2}$

Step 6(a):

$\frac{x+9}{x}=9$

Step 7(a):

x + 9 = 9x

Step 8(a):

9 = 8x

Step 9(a):

$x=\frac{9}{8}$

Step 1(b):

500(1.15)²^x^{− 1} = 9000

Step 2(b):

(1.15)²^x^{− 1} = 18

Step 3(b):

log(1.15)²^x^{− 1} = log18

Step 4(b):

(2x − 1)log(1.15) = log18

Step 5(b):

$(2x-1)=\frac{\text{log}18}{\text{log}(1.15)}$

Step 6(b):

$x=\frac{\text{log}18}{2\text{log}(1.15)}+1$

Step 7(b):

x ≈ 10.82