Question

Write log 81 + log 64 + log 5 - log 72. In the form of log N​

Answer 1

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 $log_{a}b=x$. 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,

$=log81+log64+log5-log72$

We will use the BODMAS rule and the logarithmic rule simultaneously,

$=log81+log64+log5-log72\\=log(81*64*5)-log72\\=log(\frac{81*64*5}{72} )\\=log360$

Hence, the value of log 81 + log 64 + log 5 - log 72 in the form of log N​ is log 360.