How do you use the Change of Base Formula and a calculator to evaluate the logarithm ${log}_{3} 48$ $log_3 48$ ?

Question

1978 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-01-12T17:03:33

≈ 3.524 (3 decimal places)

${log}_{a} x$ $log_a x$ may be converted to the base b by using the following formula :

$\frac{{log}_{b} x}{{log}_{b} a}$ $log_b x/log_b a$ (x > 1 )

In this case write ${log}_{3} 48 = \frac{{log}_{10} 48}{{log}_{10} 3}$ $log_3 48 = log_10 48 /log_10 3$

Other bases , apart from base 10 may be used. Base 10 is convenient as it can be evaluated on a calculator ( as of course can ln)

When using base 10 it is usual for it to be written without the 10.

$\Rightarrow \frac{{log}_{10} 48}{{log}_{10} 3} = \frac{log 48}{log 3}$ $rArr log_10 48/log_10 3 = log 48/log 3$

using the log key on a calculator (this is to base 10 )

$\Rightarrow \frac{log 48}{log 3} = \frac{1.68124}{0.47712} \approx 3.524$ $rArr log48/log3 = 1.68124/0.47712 ≈3.524$

How do you use the Change of Base Formula and a calculator to evaluate the logarithm log_3 48log348log_3 48?