There are logarithmic formulas and identities which can help us in solving logs without having to use a calculator.
Let us take an example and look at how the identities can be used to solve logs without the help of a calculator.
Suppose we need to find the value of log 128 to the base 8, that is -
[tex]log_{8} 128[/tex]
Now, according to a property of logs -
Thus we have,
[tex]log_{8} 128[/tex] [tex]= log_{2^{3} } 2^{7}[/tex]
= [tex]7/3(log_{2 } 2)[/tex]
another property of logs is -
[tex]log_{a} a[/tex] = 1
⇒ [tex]7/3(log_{2 } 2)[/tex] = 7/ 3 × 1
= 7/3
Thus, we found out the value of a log without using a calculator. We can similarly use logarithmic properties to solve logs without using a calculator.
Learn more about logs here-
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