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all right the next example ladies and gentlemen we have 6 times e raised to the negative x equals 3. again isolate the variable so in this case i divide by 6 on both sides i have e to the negative x equals one-half now like in my last example to get rid of the log base to get rid of base 10 or 10 as my exponent i took the log of base 10. well here im going to have to take the log of base what which the log of base e is what we call actually just ln of e which is your natural logarithm so i am going to take the ln a base e ln is basically but ill write it in there as well so you take the ln of both sides because ladies and gentlemen ln base e of e raised to the negative x equals ln base e of one half if you guys remember in your notes at the beginning of class i gave an example of this ln base e of e raised to the negative x is just going to equal negative x which is equal to ln base e of one half again i keep on writing in the base e but we dont have to because your calculator is al