Processing Math: Done

From Förberedande kurs i matematik 1

Before we even start thinking about transforming log2 and log3 to ln, we use the log laws

lgab=blga

lgab=lga+lgb 

to simplify the expression

log3log23118=log3118log23=log3118+log3log23 

With help of the relation

2log2x=x and 3log3x=x

and taking the natural logarithm , we can express log2 and log3 using ln,

log2x=lnxln2 and log3x=lnxln3

The two terms log3 118 and log3 log2 3 can therefore be written as

log3118=ln3ln118 and log3log23=log3ln2ln3 

where we can simplify the last expression further with the logarithm law, log a/b = log a – log b, and then transform log3 to ln,

log3ln2ln3=log3ln3−log3ln2=ln3lnln3−ln3ln2 

In all, we thus obtain

log3log23118=ln3ln118+ln3lnln3−ln3ln2

Input into the calculator gives

log3log231184762

NOTE: the button sequence on a calculator will be:

118LN3LN+3LNLN3LN−2LNLN3LN=