Question

log12/13-log7/25+log91/3

Answer 1

(log 12/13/7/25)+log91/3
log300/91+log91/3

;log(300/91 × 91/3)

;log 100
;log10×log10
;1×1=1

Answer 2

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

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

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

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

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

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

$\displaystyle \sf{ = log \: 100 }$

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

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

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

$\displaystyle \sf{ = 2 \times 1 }$

$\displaystyle \sf{ = 2 }$

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ if 2log x base y=6,then the relation between x and y

https://brainly.in/question/27199002

2.If 2log((x+y)/(4))=log x+log y then find the value of (x)/(y)+(y)/(x)

https://brainly.in/question/24081206