Hi



 4^4 = (2x-7)(3x-3)

  6x^2 -27x + 21 - 256 = 0

  3x^2 - 27x -235 = 0



 x: -4.7,  9.2  (rounded to the nearest tenth)

 

Answer by jsmallt9(3758)   (Show Source): You can put this solution on YOUR website!
 Assuming these are base 4 logarithms...



We want the equation in the form

log(expression) = other-expression

So we will use a property of logarithms, , to combine the logarithms:




Now that the equation is in the desired form, the next step is to rewrite the equation in exponential form. In general  is equivalent to . Using this pattern on our equation we get:



which simplifies to:




Now that the variable is out of the logarithm, we can solve for it. This is a quadratic equation so we want one side to be zero. Subtracting 256 from each side:



Next we factor or use the Quadratic Formula. This will not factor so we must use the formula:



Simplifying...











So  or 


Since you were asked for decimal answers, get out your calculator and round off your answer to the nearest tenth.



 

Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
 Use the general rule:



Also, express the right side as a log to base 4















 







 

 

 

 

 







To nearest tenth, 

check answer:













Looks close enough

-----------------

Note that  had to be positive because a log

with a positive base (4), can't result in a negative number 

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