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Business Mathematics and Basic Statistics · Class 12 Commerce

Ch 4Logarithms — Class 12 Business Mathematics and Basic Statistics, concept-first.

This WBCHSE Class 12 Commerce Business Mathematics and Basic Statistics chapter introduces the logarithm — a tool that answers the question exponentiation cannot ask directly: given a base and a result, what exponent produced that result?

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Q&A

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Concepts

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Key concepts

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Logarithm as the Inverse of Exponentiation

means exactly (for ) — a logarithm IS the exponent needed to turn the base into . and hold for every valid base.

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Chapter contents

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1

Logarithm as the Inverse of Exponentiation

This WBCHSE Class 12 Commerce Business Mathematics and Basic Statistics chapter introduces the logarithm — a tool that answers the question exponentiation cannot ask directly: given a base and a resul…

2

Laws of Logarithms — Product, Quotient, and Power Rule

Because a logarithm is exactly an exponent, every law of logarithms below is really the corresponding law of INDICES, translated into logarithm language.

3

Change-of-Base Formula

Sometimes a logarithm needs to be evaluated in a base for which the value isn't directly known or easy to compute (e.g. ), while an equivalent calculation in a DIFFERENT, more convenient base (e.g.

4

Common Logarithm and Natural Logarithm

A logarithm to base is called a common logarithm, usually written without showing the base at all:

5

Solving Simple Logarithmic and Exponential Equations

The fastest way to solve a simple equation involving a logarithm is often to rewrite it in exponential form using the definition directly: . For example, becomes immediately.

Exercises

+Show 5 questions5 questions
  1. Q8Evaluate: (i) $\log_7 1$ (ii) $\log_9 9$.Free
  2. Q9Given $\log 5 = 0.6990$, simplify $\log_{10} 20 - \log_{10} 4$ and evaluate it.Free
  3. Q10Solve for $x$: $\log_2(x+1) = 3$.Preview
  4. Q11Evaluate $\ln e^5$.Preview
  5. Q12Solve for $x$: $\log x + \log(x-3) = 1$ (common logarithm, base 10).Preview

More questions

+Show 7 questions7 questions
  1. Example 1Express $3^4=81$ in logarithmic form.Free
  2. Example 2Evaluate $\log_2 32$.Free
  3. Example 3Evaluate $\log_{10} 1000$.Free
  4. Example 4Given $\log 2 = 0.3010$ and $\log 3 = 0.4771$, find $\log 6$.Preview
  5. Example 5Simplify $\log_2\left(8^5\right)$.Preview
  6. Example 6Evaluate $\log_4 64$ using the change-of-base formula (change to base 2).Preview
  7. Example 7Solve for $x$: $\log_3 x = 4$.Preview