Question

The correct value of log255 - log497 is

Answer 1

Answer:

log255-log497.

log255=2.40654018.

log497=2.696356.

log255-log497=2.40654018-2.696356.

=-0.28981582.

I think this is your answer.

Answer 2

$\displaystyle \sf{ log_{5} \: 25 - log_{7} \:49 } = 0$

Given :

$\displaystyle \sf{ log_{5} \: 25 - log_{7} \:49 }$

To find :

The value of the expression

Formula :

We are aware of the formula on logarithm that

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

$\sf{2. \: \: log_{a}(a) = 1}$

Solution :

Step 1 of 2 :

Write down the given expression

Here the given expression is

$\displaystyle \sf{ log_{5} \: 25 - log_{7} \:49 }$

Step 2 of 2 :

Find the value of the expression

$\displaystyle \sf{ log_{5} \: 25 - log_{7} \:49 }$

$\displaystyle \sf{ = log_{5} \: ( {5}^{2} )- log_{7} \:( {7}^{2} ) }$

$\displaystyle \sf{ = 2log_{5} \: 5 - 2 log_{7} \:7 }\: \: \: \bigg[ \: \because \: log( {a}^{n} ) = n log(a)\bigg]$

$\displaystyle \sf{ = (2 \times 1) -(2 \times 1) }\: \: \: \bigg[ \: \because \:log_{a}(a) = 1 \bigg]$

$= 2 - 2$

$= 0$

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