SOLUTION: 1+log bas4 (X-1)=log base2 (X-9)

Question 824222: 1+log bas4 (X-1)=log base2 (X-9)
Answer by math-vortex(648) (Show Source): You can put this solution on YOUR website!

Hi, there--

YOUR PROBLEM:
Sove for x.


SOLUTION:
Use the change of base formula to convert the lot expressions to the same base.



Notice that  because . So, we simplify,





Apply the Log Law for Subtraction/Division and the Log Law for Powers


Translate the logarithmic equation into the related exponential equation.


Simplify.


}

Solve this quadratic equation by factoring.

 OR 

Always check your answers for extraneous roots.

For x = 17:




 TRUE

For x = 5:




Here we have a problem because the logarithm of a negative number is not part of the set of 
real numbers. (There is no real exponent to which you can raise the base 2 and get -4.) Thus 
x=5 is not a solution to this equation.

Hope this helps, and I'm very sorry for the delay!

Ms. Figge
math.in.the.vortex@gmial.com

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