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Math Help - Please solve these equations!

  1. #1
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    Lightbulb Please solve these equations!

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