Math, asked by jackiechan5797, 19 days ago

Log 81 +log 64+log 5-log 72 in the form of log N

Answers

Answered by sonalminz
17

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.

I hope this will help you :)

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