How do you use the Change of Base Formula and a calculator to evaluate the logarithm ${log}_{4} 24$ $log_4 24$ ?

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Answer 1 · 2018-06-12T02:35:36

Below

The change of base formula is given by: ${log}_{a} b = \frac{{log}_{10} b}{{log}_{10} a}$ $log_ab = log_10b/log_10a$

Looking at ${log}_{4} 24$ $log_4 24$ , we can tell that a=4 and b=24.

${log}_{4} 24 = \frac{{log}_{10} 24}{{log}_{10} 4} = 2.292$ $log_4 24 = log_10 24/log_10 4 = 2.292$

Answer 2 · 2018-06-12T07:46:29

$y = 2.29248$ $y=2.29248$ (5 dps)

from first principles

$y = {log}_{4} 24$ $y=log_4 24$

$\Rightarrow 4^{y} = 24$ $=>4^y=24$

take logs to both sides ( we will use base 10)

${log 4}^{y} = log 24$ $log4^y=log24$

$y log 4 = log 24$ $ylog4=log24$

$y = \frac{log 24}{log 4}$ $y=log24/log4$

$y = 2.29248125$ $y=2.29248125$

note: some calculators now have a function that can evaluates logarithms in any base

How do you use the Change of Base Formula and a calculator to evaluate the logarithm log424log_4 24?