How to Simplify this Complex Logarithm Expression?

In summary: Therefore, it is in your best interest to make your questions clear and interesting. Click to expand...​In summary, the given expression $( \log_{a}\left({b}\right)+\log_{b}\left({a}\right)+2) (\log_{a}\left({b}\right)-\log_{ab}\left({b)}\right)* \log_{b}\left({a}\right)-1=$ does not have a specific numerical value, as it contains variables $a$ and $b$. It can be simplified to $\log_{b}\left({a^{2}}\right)+1$.
  • #1
Elena1
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1) $( \log_{a}\left({b}\right)+\log_{b}\left({a}\right)+2) (\log_{a}\left({b}\right)-\log_{ab}\left({b)}\right)* \log_{b}\left({a}\right)-1=$?
 
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  • #2
Elena said:
1) ( \log_{a}\left({b}\right)+\log_{b}\left({a}\right)+2) (\log_{a}\left({b}\right)-\log_{ab}\left({b)}\right)* \log_{b}\left({a}\right)-1=?

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FAQ: How to Simplify this Complex Logarithm Expression?

What is a logarithm?

A logarithm is a mathematical function that helps us solve exponential equations. It is the inverse function of exponentiation.

What does it mean to simplify a logarithm?

Simplifying a logarithm means to rewrite it in a simpler form. This usually involves using the properties of logarithms to combine or break down terms.

What are the rules for simplifying logarithms?

There are several rules for simplifying logarithms, including the product rule, quotient rule, power rule, and change of base rule. These rules allow us to manipulate the terms inside a logarithm to make it simpler.

What is the value of log 3?

The value of log 3 is approximately 0.477. This can be found by evaluating log 3 on a calculator or by using the definition of a logarithm.

How can I simplify log 3 without a calculator?

You can simplify log 3 by using the rules of logarithms, such as the product rule or power rule. You can also use the definition of a logarithm and rewrite it as an exponential equation to solve for the value of log 3.

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