SOLUTION: Can I please get help solving these equations to find the value of x and can I please see the working as I am unsure of how to solve them: i)e^2x + 5e^x + 6 = 0 ii) ln (x+4)

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Question 1106424: Can I please get help solving these equations to find the value of x and can I please see the working as I am unsure of how to solve them:
i)e^2x + 5e^x + 6 = 0
ii) ln (x+4) + ln(x-2) = ln 7
iii) 3 tan^3 (x) - 3 tan^2 (x) - tan (x) + 1 = 0
Thanks :)
Answer by greenestamps(13200) (Show Source):
You can put this solution on YOUR website!

(1)
squared is , so this is a "quadratic" in which the "variable" is . So factor it like a quadratic:

and solve from there.

However, you don't really need to do anything algebraically with this one if you think about it. Both and are always positive, so the left side of the equation is always positive; that of course means the solution set will be empty.

(2)
Use your rules of logarithms. The sum of logs is the log of the product:

If the logs are equal, then the expressions are equal:

This is a quadratic which you can solve by any of a number of methods.

(3)
The most common way of factoring an expression with four terms is by grouping. Take the common factor out of the first two terms to give you an idea of what to do with the last two terms.

There is now a common factor of , so

or
And again finishing from there should be easy.