Solve the equation log (little 3) X + log (little6) X = 2

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In summary, the equation log (little 3) X + log (little 6) X = 2 can be solved by using the properties of logarithms to simplify the expression and then solving for x. The final answer is approximately 3.9. It is important to note that the answer given in the conversation, 7.2 and -1.2, is incorrect.
  • #1
jupiter_8917
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Solve the equation

log (little 3) X + log (little6) X = 2
the answer is 3.9

Here is what I try
log (little 6)x = log (little 3)x/log (little 3)6 = log (little 3) (x-6)log (little 3)x + log (little 3) (x-6) = 2
log (little3) (x(x-6)) =2
log (little3) (x^2-6x)=3^2

x^2 -6x =9
x^2-6x-9=0

x= 7.2 and -1.2 and of course it is not the right answer

can anyone please explain how do you get 3.9? Thank you
 
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  • #2
jupiter_8917 said:
Here is what I try
log (little 6)x = log (little 3)x/log (little 3)6 = log (little 3) (x-6)
Thank you

log6(x)=log3(x) /log3(6)- this is right,
but it is not equal to log3(x-6).

ehild
 

FAQ: Solve the equation log (little 3) X + log (little6) X = 2

1. What does the equation log (little 3) X + log (little6) X = 2 mean?

The equation log (little 3) X + log (little6) X = 2 is a logarithmic equation that is asking us to solve for the value of X that satisfies the equation. The logarithmic notation means that we are looking for the power to which the base (3 and 6 in this case) must be raised to equal 2.

2. How do I solve logarithmic equations like log (little 3) X + log (little6) X = 2?

To solve logarithmic equations, we can use the properties of logarithms to rewrite the equation into a simpler form. In this case, we can use the product rule of logarithms to combine the two logarithms into one, giving us log (little 3)(little 6) X = 2. Then, we can use the exponent rule to rewrite the equation as (little 3)(little 6)^2 = X, which simplifies to X = 108.

3. Can I check my answer to the equation log (little 3) X + log (little6) X = 2?

Yes, you can check your answer by plugging it back into the original equation and seeing if it satisfies the equation. In this case, if we plug in X = 108, we get log (little 3) 108 + log (little6) 108 = 2, which is true.

4. Are there any restrictions on the values of X in the equation log (little 3) X + log (little6) X = 2?

Yes, there are restrictions on X in this equation. Since logarithms are only defined for positive numbers, X must be a positive number. Additionally, the base of a logarithm cannot be equal to 1, so X cannot be equal to 1.

5. Can I solve this equation without using logarithms?

No, this equation is a logarithmic equation and cannot be solved without using logarithms. Logarithms are necessary to isolate the variable X in the equation and find its value. However, there may be alternative methods to solve the equation that do not involve using logarithms explicitly.

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