Evaluating logarithms using change-of-base formula

Examples0/7

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Examples

Lessons

How to apply $``$ $‘‘$ change-of-base rule $"$ $"$

Express $\log_53$ $lo g_{5} 3$ in three different ways.
Using a calculator, evaluate the following logarithms
by applying $``$ $‘‘$ change-of-base rule $":$ $" :$
1. $\log_53$
2. $\log_7\sqrt{416}$
3. $\log_2\frac{7}{25}$
4. 6 $\log_4999$
Using a calculator, solve for $x$ $x$ to the nearest hundredth.
1. $\log_6x = log_7 8$
2. $\log_{23}5 = log_x\sqrt{0.104}$

Topic Notes

• change-of-base rule:

\log_ba = \frac{\log_xa}{\log_xb} = \frac{\log a}{\log b}

• common logarithms:

log with base

``10"

example:

\log3 = \log_{10}3

example:

\log x = \log_{10}x

Basic Concepts

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