Solving Logarithmic Equations: How to Find the Value of x

  • Thread starter HalloGubi
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In summary, the conversation is about solving the equation logx+log(x+3)=1 and using the properties of logarithms and factoring quadratics to find the solution.
  • #1
HalloGubi
2
0

Homework Statement



logx+log(x+3)=1

Homework Equations





The Attempt at a Solution



Ive tried to put it in solve so i know x=2

i think i have to, hmm i don't know if its called differantiate in english but i don't know how to differantiate log.


Edit: this is what I've tried after differantiating

1/x+1/x=1
that means it must be 2 since 2 halfs give 1
 
Last edited:
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  • #2


Welcome to Physics Forums.

I'm guessing that you're trying to solve for equation to find x?
 
  • #3


yes, sry for my bad explaining of my problem
 
  • #4


HalloGubi said:
yes, sry for my bad explaining of my problem
No problem.

When attempting to solve equations, usually the best thing to do is to collect all the terms you want together. So can you combine the two log terms into a single logarithm?
 
  • #5


HalloGubi said:

Homework Statement



logx+log(x+3)=1

Homework Equations





The Attempt at a Solution



Ive tried to put it in solve so i know x=2

i think i have to, hmm i don't know if its called differantiate in english but i don't know how to differantiate log.


Edit: this is what I've tried after differantiating

1/x+1/x=1
that means it must be 2 since 2 halfs give 1

This problem has nothing to do with differentiation. All you need to know are the properties of logarithms and how to factor quadratics.
 
  • #6


I know this is an old post but incase people find it in the future:

rule 1)
logbx + logby = logbxy

rule 2)
x (x + a) = x2 + ax

rule 3)
solving quadratic equations
 

1. What does the equation log(x) + log(x+3) = 1 mean?

The equation log(x) + log(x+3) = 1 is a logarithmic equation, which means it involves the use of logarithms. In this specific equation, x represents the base of the logarithm and the term (x+3) represents the argument of the logarithm. The equation is asking you to find the value of x that will satisfy the equation when plugged into the logarithmic function.

2. How do I solve log(x) + log(x+3) = 1?

To solve this equation, you can use the properties of logarithms. The first step is to combine the two logarithms using the product property, which states that log(a) + log(b) = log(ab). So, in this case, the equation can be rewritten as log(x(x+3)) = 1. Then, using the definition of logarithms, the equation can be rewritten as x(x+3) = 10^1. Simplifying further, the equation becomes x^2 + 3x - 10 = 0. Solving this quadratic equation will give you the two possible values of x.

3. What is the significance of the logarithmic function in this equation?

The logarithmic function is used in this equation to solve for the unknown variable, x. Logarithms are useful because they allow us to solve for an unknown exponent or power in an equation. In this case, the logarithmic function helps us to solve for the value of x that satisfies the equation.

4. Can this equation have more than one solution?

Yes, this equation can have more than one solution. In fact, quadratic equations, such as the one in this equation, can have two solutions. In the case of this specific equation, the two solutions will be the values of x that make the equation true when plugged into the logarithmic function.

5. Is there a specific method or formula to solve this equation?

Yes, there are specific methods and formulas that can be used to solve this equation. As mentioned before, the properties and definitions of logarithms can be used to simplify the equation and solve for the unknown variable. Additionally, there are other methods, such as the quadratic formula, that can be used to solve for the solutions of a quadratic equation like this one.

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