Question

How do you solve \[\log n=1.8\]?

Answer 1

Hint: The logarithm is the inverse function to exponentiation that means the logarithm of a given number \[n\] is the exponent to which another fixed number the base \[b\], must be raised to produce that number \[x\]. In the simplest case the logarithm counts the number of occurrences of the same factor in repeated multiplication. By using the logarithm definition we can solve this.

Complete step by step solution:
We have given \[\operatorname{logx}=1.8\]
\[\log n\]means \[{{\log }_{10}}x\]
The base of the \[\log \] is \[10\]
By definition \[{{\log }_{b}}x=y\] is equivalent to \[{{b}^{y}}=x\]
Therefore \[{{\log }_{10}}x=1.8\] is equivalent to \[{{10}^{1.8}}=x\]
(Which can be evaluated using a calculator as approximately \[63.096\])
\[x={{10}^{1.8}}\cong 63.096\]

Note: For solving \[\log \] problems you must know all \[\log \] rules and try to memorise them. Don’t forget the base of \[\log \] when not given in the problem is always \[10\]. By solving the problem, it will be easier for you.