CPM Homework Help : PC Problem 8-127

Use properties of logs to solve each of the following equations. Use exact values. Homework Help ✎
1. log(x + 3) = 2
2. ln(x + 3) = 2
3. ln 3 + ln(x) = 4
4. ln(x + 4) − ln(x) = 2

Answer (a):

10^log(^x⁺³⁾ = 10²
x + 3 = 100
x = 97

Hint (b):

e^log(^x⁺³⁾ = e²

Hint (c):

ln(3x) = 4
e^ln(3^x⁾ = e⁴

Steps (d):

$\text{ln}\frac{x+4}{x}=2$

$e^{\text{ln}\frac{x+4}{x}}=e^{2}$

$\frac{x+4}{x}=e^{2}$

x + 4 = xe²
x − xe² = −4
x(1 − e²) = −4

Answer (d):

$x=\frac{-4}{1-e^{2}}\Rightarrow \frac{4}{e^{2}-1}$