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Thread: Logarithm Equation

  1. #1
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    Logarithm Equation

    Hi, can you please help me to understand a portion of this example. I am ok until the 4th line that uses the distributive property. Should I distribute the ln alone or do I distribute the ln 2?

    Again, itís line 4 that I have a problem understanding. I think I could figure out the rest once I understand line 4.

    Thanks for your help with this one.
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  2. #2
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    Hello, coopsterdude!

    Can you please help me to understand a portion of this example?
    I am ok until the 4th line that uses the distributive property.
    Should I distribute the ln alone or do I distribute the ln 2?


    $\displaystyle 2^{2x-1} \;= \;3^x$

    $\displaystyle \ln(2^{2x-1}) \;= \;\ln(3^x)$

    $\displaystyle (2x - 1)\cdot\ln 2 \;= \;x\cdot\ln 3$

    $\displaystyle 2x\cdot\ln 2 - \ln 2 \;= \;x\cdot\ln 3$ . . . Distributive Property


    Don't you see anything wrong with this?

    . . $\displaystyle (2x - 1)\cdot\ln 2 \;= \;(2x\cdot\ln - \ln)\cdot 2$


    Think about what you're asking . . .

    If I have: .$\displaystyle (x + 7)\cdot\sqrt{3}$,

    . . can I distribute the $\displaystyle \sqrt{\;\;}$ and leave the $\displaystyle 3$ outside

    . . and get: .$\displaystyle (x\sqrt{\;\;} + 7\sqrt{\;\;})\cdot3$ ?

    Oh, sure . . . why not?

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  3. #3
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    Thanks Soroban, that's how I would have done the distribution. Isolating the x in that way led to my confusion. Thanks for you help.
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