Question

evaluate the foolwing log7(49)

Answer 1

Actually log of a number (in this case 49) to a base (in this case 7) is the number which should be placed in the power of base to obtain the number whose log is being taken. 

So, 7^2 = 49. 

Hence, log7 49 = 2

hope its helpful to you

Answer 2

$\displaystyle \sf{ log_{7}(49) } = 2$

Given :

The expression

$\displaystyle \sf{ log_{7}(49) }$

To find :

The value of the expression

Formula :

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

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

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is

$\displaystyle \sf{ log_{7}(49) }$

Step 2 of 2 :

Find the value of the expression

$\displaystyle \sf{ log_{7}(49) }$

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

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

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

$= 2$

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