Solve log(base4)X + log(base4) (X+6) <2

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In summary, the conversation discusses solving a logarithmic inequality using relevant equations. The solution involves determining potential solutions for x and applying relevant equations to solve the inequality.
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VVVS
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Homework Statement


Solve log(base4)X + log(base4) (X+6) <2


Homework Equations


log(base4)X + log(base4) (X+6) =2 comes out to x=-8 and X=2


The Attempt at a Solution


I can't seem to figure out what steps I should even take to answer this inequality.
 
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  • #2


this property should be useful:
[tex]log_a (b*c) = log_a b + log_a c[/tex]
applying this to your inequality and changing 2 into [tex]log_4 16[/tex] you'll get something that can be easily transferred into inequality containing quadratic function, which you'll surely solve on your own
 
  • #3


VVVS said:

Homework Statement


Solve log(base4)X + log(base4) (X+6) <2


Homework Equations


log(base4)X + log(base4) (X+6) =2 comes out to x=-8 and X=2
One relevant equation here would be logaA + logaB = logaAB.
Another is logab = c <==> b = ac.
The equation you have here is part of your work, not really a relevant equation.
VVVS said:

The Attempt at a Solution


I can't seem to figure out what steps I should even take to answer this inequality.

First off, you should determine which values of x are going to be allowed as potential solutions. Then, see if the equations I added might be of some help to you.
 

FAQ: Solve log(base4)X + log(base4) (X+6) <2

What is the first step in solving this logarithmic inequality?

The first step is to combine the two logarithms using the product rule, which states that log(a) + log(b) = log(ab). This will result in a single logarithm with the product of the two terms inside.

How do I get rid of the logarithm on the left side of the inequality?

To eliminate the logarithm, we can raise both sides of the inequality to the base of the logarithm, which in this case is 4. This will result in a simpler linear inequality that can be solved algebraically.

Is there anything special I need to do when raising both sides of the inequality to the base of the logarithm?

Yes, we need to keep in mind that raising to a power of a logarithm is equivalent to taking the inverse operation of the logarithm. In this case, we need to take the inverse logarithm on both sides, which is 4 raised to the power of each side.

What is the final step in solving this inequality?

The final step is to solve the resulting linear inequality by isolating the variable on one side and all other terms on the other side. This will give us the solution set for the original logarithmic inequality.

How do I check my answer to ensure it is correct?

To check the solution, we can plug the value of the variable into the original inequality and see if it satisfies the inequality. If it does, then the solution is correct. We can also graph the original inequality and see if the solution falls within the shaded region on the graph.

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