Original
Compute {{MATH_13}} using logarithms.
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Start by writing both numbers in scientific notation
{{MATH_15}}
Next we use a log-table, which gives {{MATH_16}} for values of
{{MATH_17}} ranging between {{MATH_18}} and {{MATH_19}}. We've reproduced part of such a
table below.
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From the table, we see that
{{MATH_23}}
Add these numbers together to get {{MATH_24}}.
Essentially, we know the following at this point:
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Using the table again, we see that
{{MATH_28}}. Since we were
working in scientific notation, we need to multiply this by
{{MATH_29}}. Our final answer is
{{MATH_30}}
Since {{MATH_31}}, this is a good approximation.
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The moral is:
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{{CMD_35}}Logarithms allow us to use addition in place of multiplication.{{CMD_36}}
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