Math, asked by kajal205paml6y, 1 year ago

log12/13-log7/25+log91/3

Answers

Answered by shpriyanshu
2
(log 12/13/7/25)+log91/3
log300/91+log91/3

;log(300/91 × 91/3)

;log 100
;log10×log10
;1×1=1
Answered by pulakmath007
0

\displaystyle \sf{ log  \:  \frac{12}{13}   - log \:  \frac{7}{25} +  log \:  \frac{91}{3}  }

Given :

\displaystyle \sf{ log  \:  \frac{12}{13}   - log \:  \frac{7}{25} +  log \:  \frac{91}{3}  }

To find :

The value of the expression

Formula :

We are aware of the formula on logarithm that

 \sf{1.  \:  \: \:  log( {a}^{n} ) = n log(a)  }

 \sf{2. \:  \:  log(ab) =  log(a)   +  log(b) }

 \displaystyle \sf{3. \:  \:  log \bigg( \frac{a}{b}  \bigg)  =  log(a) -  log(b)  }

 \sf{4. \:  \:   log_{a}(a)   = 1}

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is

\displaystyle \sf{ log  \:  \frac{12}{13}   - log \:  \frac{7}{25} +  log \:  \frac{91}{3}  }

Step 2 of 2 :

Find the value of the expression

\displaystyle \sf{ log  \:  \frac{12}{13}   - log \:  \frac{7}{25} +  log \:  \frac{91}{3}  }

\displaystyle \sf{  = log  \bigg( \frac{12}{13}  \times  \frac{25}{7} \bigg) +  log \:  \frac{91}{3}  }

\displaystyle \sf{  = log  \bigg( \frac{12}{13}  \times  \frac{25}{7}  \times  \frac{91}{3} \bigg)  }

\displaystyle \sf{  = log  \bigg( 4 \times 25 \bigg)  }

\displaystyle \sf{  = log   \: 100  }

\displaystyle \sf{  = log_{10}(100)   }

\displaystyle \sf{  = log_{10}( {10}^{2} )   }

\displaystyle \sf{  =2 log_{10}( {10}^{} )   }

\displaystyle \sf{  = 2 \times 1  }

\displaystyle \sf{  = 2 }

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