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

  • Thread starter Thread starter VVVS
  • Start date Start date
AI Thread Summary
To solve the inequality log(base4)X + log(base4)(X+6) < 2, it can be transformed using the property log_a(b*c) = log_a b + log_a c. This leads to the equivalent form log(base4)(X(X+6)) < log(base4)(16). The solutions to the equation log(base4)X + log(base4)(X+6) = 2 yield x = -8 and x = 2. It is essential to determine the valid values of x that satisfy the initial inequality. The discussion emphasizes the need to apply logarithmic properties and analyze potential solutions effectively.
VVVS
Messages
2
Reaction score
0

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.
 
Physics news on Phys.org


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


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.
 

Thread 'Finding the number of ways to arrange identical balls in a circle (3 different colors)'

I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
View full post »

Thread 'Greatest possible value of a constant in polynomial'

Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
View full post »

Similar threads

Solve the given equation that involves fractional indices
Replies
39
Views
3K
Is there a rule that states that I should not divide in this scenario?
Replies
10
Views
1K
How to graph by hand: y=log((x/(x+2))
Replies
3
Views
1K
Determine whether a logarithmic function is odd or even
Replies
11
Views
6K
Rearranging Logarithms: Finding the Solution to log Equations
Replies
10
Views
3K
Solving for x in 3^(log(base4)x)
Replies
3
Views
1K
Log inside log -- find the x in its max domains?
Replies
10
Views
2K
Approximation used in physics explanation
Replies
8
Views
2K
Why (a log x = b log x / b log a)?
Replies
11
Views
3K
Solve for x: 2^3+2^3+2^3+2^3=2^x
Replies
3
Views
2K

Hot Threads

Recent Insights

Back
Top