Log 81 +log 64+log 5-log 72 in the form of log N
Answers
Answer:
Given:
log 81 + log 64 + log 5 - log 72
To Find:
To express in the form of log N
Solution:
Before simplifying the given equation we should what logarithm is and what are the basic rules we use for the logarithmic equation.
A logarithm is the inverse function of an exponential function expressed in the form of a^x=b which in logarithm is expressed as log_{a}b=xlog
a
b=x . The basic rules we use are
- log A*B= log A + log B ( when two logs are added together then their values gets multiplied )
- log(A/B)= log A - log B ( when two logs are subtracted then their values gets divided)
Now using the given rules to find the value of the given equation we have,
=log81+log64+log5-log72=log81+log64+log5−log72
We will use the BODMAS rule and the logarithmic rule simultaneously,
\begin{gathered}=log81+log64+log5-log72\\=log(81*64*5)-log72\\=log(\frac{81*64*5}{72} )\\=log360\end{gathered}
=log81+log64+log5−log72
=log(81∗64∗5)−log72
=log(
72
81∗64∗5
)
=log360
Hence, the value of log 81 + log 64 + log 5 - log 72 in the form of log N is log 360.