• January 15th 2008, 12:57 PM
rlarach
1. 2.7^x = 4
2. ln x - ln(3x - 5) = 2
• January 15th 2008, 01:09 PM
mr fantastic
Quote:

Originally Posted by rlarach
1. 2.7^x = 4
2. ln x - ln(3x - 5) = 2

1. Take ln of both sides. Then use the rule $\ln a^n = n \ln a$ to get a linear equation in x. Then solve for x. $x = \frac{4}{\ln 2.7} \approx$ a decimal approximation you can get from any calculator with a ln button.

2. Combine the two logs on the left using the rule $\ln a - \ln b = \ln \frac{a}{b}$. Exponentiate both sides to the base e and then use the rule that $e^{\ln \text{(stuff)}} = \text{stuff}$. Now multiply both sides by (3x - 5) to get a linear equation in x:

$x = e^2 (3x - 5)$

Expand, re-arrange to group like terms and solve for x. $x = \frac{5}{3e^2 - 1} \approx$ a decimal approximation you can get from any calculator with an $e^x$ button.