How to Solve This Logarithmic Problem?

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In summary, a logarithm is an operation that is the inverse of exponentiation and is used to solve for the unknown power in an exponential equation. The most common way to solve a logarithm is by using the properties of logarithms and rewriting the expression in exponential form. The base of a logarithm is the number raised to a power in an exponential expression. An example of solving a logarithm is log3(x) = 2, which can be rewritten as 3^2 = x, giving x = 9. It is important to be aware of rules such as the inverse relationship between logarithms and exponentials, the change of base rule, and the natural logarithm rule when solving logarithms.
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phy_
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show how
 
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Multiply both sides by 2, 2*log((x-y)/3)=log(x)+log(y). Now what? Show us what you try.
 
  • #3
log((x - y)/3) = 1/2(log x + log y)
==> log((x - y)/3) = 1/2(log xy)
==> log((x - y)/3) = log (xy)1/2

Now, if the logs of two numbers are equal, then the two numbers must be equal. (Equivalently you could exponentiate each side of the equation; that is, make each side the exponent on 10. 10log a = a as long as a > 0.
 
  • #4
Thank-you so much.
 

Related to How to Solve This Logarithmic Problem?

1. What is a logarithm?

A logarithm is an operation that is the inverse of exponentiation. It is used to solve for the unknown power in an exponential equation.

2. How do I solve a logarithm?

The most common way to solve a logarithm is by using the properties of logarithms, such as the product rule, quotient rule, and power rule. It is also helpful to rewrite the logarithmic expression in exponential form.

3. What is the base of a logarithm?

The base of a logarithm is the number that is raised to a power in an exponential expression. For example, in the expression log28, the base is 2.

4. Can you provide an example of solving a logarithm?

Sure! Let's say we have the equation log3(x) = 2. To solve for x, we can rewrite this in exponential form as 32 = x. Therefore, x = 9.

5. Are there any rules I should be aware of when solving logarithms?

Yes, there are a few important rules to keep in mind when solving logarithms. These include the inverse relationship between logarithms and exponentials, the change of base rule, and the natural logarithm rule. It is important to review and understand these rules before attempting to solve logarithms.

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