Question

Find the value of log (1/2401) to the base 7​

Answer 1

Answer:

answer for the given problem is 4

Answer 2

$\displaystyle \sf{ log_{7} \bigg( \frac{1}{2401} \bigg) } = - 4$

Given :

$\displaystyle \sf{ log_{7} \bigg( \frac{1}{2401} \bigg) }$

To find :

The value of the expression

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is

$\displaystyle \sf{ log_{7} \bigg( \frac{1}{2401} \bigg) }$

Step 2 of 2 :

Find the value of the expression

$\displaystyle \sf{ log_{7} \bigg( \frac{1}{2401} \bigg) }$

$\displaystyle \sf{ = log_{7} \: 1 - log_{7} \: 2401 }$

$\displaystyle \sf{ = 0 - log_{7} \: (7 \times 7 \times 7 \times 7) }$

$\displaystyle \sf{ = - log_{7} \: ( {7}^{4} ) }$

$\displaystyle \sf{ = - 4 log_{7} \: 7 }$

$\displaystyle \sf{ = - 4 \times 1 }$

$\displaystyle \sf{ = - 4}$

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