<h2>Simplification of Logarithms</h2>
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<h2>Example</h2>
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<h3>Question</h3>
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<p>Simplify (without a calculator): \(3\log3+\log125\)</p>
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<h3>Apply the appropriate logarithmic laws to simplify the expression</h3>

\begin{align*} 3\log3+\log125 &amp;= 3\log3+\log{5^{3}} \\ &amp;= 3\log3 + 3\log{5} \\ &amp;= 3 ( \log3 + \log{5} ) \\ &amp;= 3 \log{(3 \times 5)} \\ &amp;= 3 \log{15} \end{align*}</div>
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<h3>Write the final answer</h3>
<p>We cannot simplify any further, therefore \(3\log3+\log125 = 3 \log{15}\).</p>
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<p><strong>Important:</strong> All the algebraic manipulation techniques \((\times, \div, +, -\), factorisation etc.) also apply for logarithmic expressions. Always be aware of the number of terms in an expression as this will help to determine how to simplify.</p>
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Simplification of Logarithms

Mathematics studies measurement, relationships, and properties of quantities and sets, using numbers and symbols. Arithmetic, algebra, geometry, and calculus are popular topics in mathematics.

Mathematics

Learn about functions and relations, inverse functions, exponential functions, logarithms, and how to graph and solve logarithmic equations in this tutorial.


Simplification of Logarithms

Simplification of Logarithms

Example

Question

Apply the appropriate logarithmic laws to simplify the expression

Write the final answer

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