Solving for X in a logarithmic equation

[Relz]

Solve for x in the following equation:

log₇ X + log₇(X-1) = log₇ 2X

Just by looking at the equation, I believe x=3. However, I am not sure how to show this.

 

[mmm4444bot]

log₇ X + log₇(X-1) = log₇ 2X

I believe x=3. However, I am not sure how to show this.

Yes, that's the correct solution. What was your reasoning? Considering your thought process may lead to a strategy for showing it.

If you would like to solve the equation algebraically, start by applying the following property to the right-hand side of the given equation.

log(A*B) = log(A) + log(B)

 

[Relz]

Yes, that's the correct solution. What was your reasoning? Considering your thought process may lead to a strategy for showing it.

If you would like to solve the equation algebraically, start by applying the following property to the right-hand side of the given equation.

log(A*B) = log(A) + log(B)

I just figured that if 2x equals x(x-1): x-1=2, therefore x must equal 3. I checked it by plugging 3 into the equation and it worked out. By following log(A*B) = log(A) + log(B), the log(A*B) would be the 2x but how do I get the other parts? A= x and B= x-1? The two multiplied together don't give me 2x. Any other hints?

 

[mmm4444bot]

2x equals x(x-1)

x(x - 1) does not equal 2x.

x(x - 1) = x^2 - x

By following log(A*B) = log(A) + log(B), the log(A*B) would be the 2x

No.

What I showed you is a property of logarithms that tells us how to rewrite the log of a product.

In other words, the expression 2x is a product. It is 2 times x.

When we have the log of a product, we can rewrite it as a sum of the log of the factors. In your case, these factors are 2 and x.

Applying the property to the given equation, we get:

log₇(x) + log₇(x - 1) = log₇(2) + log₇(x)

Now, notice that this equation contains an identical term on each side. Subtract that term from both sides, and think about the resulting equation.

 

[Relz]

x(x - 1) does not equal 2x.

x(x - 1) = x^2 - x




No.

What I showed you is a property of logarithms that tells us how to rewrite the log of a product.

In other words, the expression 2x is a product. It is 2 times x.

When we have the log of a product, we can rewrite it as a sum of the log of the factors. In your case, these factors are 2 and x.

Applying the property to the given equation, we get:

log₇(x) + log₇(x - 1) = log₇(2) + log₇(x)

Now, notice that this equation contains an identical term on each side. Subtract that term from both sides, and think about the resulting equation.

Okay, I'll try that. Thank you for all your help!