Question

Find the value of log(16807) to the base 49 - log(27) to the base 9

Answer 1

Step-by-step explanation:

Exp. = log4916807 - log927

= log72 75 - log32 33

=(5/2)log77 - (3/2)log33

=5/2 - 3/2

= 1

Answer 2

$\displaystyle \sf{ log_{49}(16807) - log_{9}(27) } = 1$

Given :

$\displaystyle \sf{ log_{49}(16807) - log_{9}(27) }$

To find :

The value of the expression

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is

$\displaystyle \sf{ log_{49}(16807) - log_{9}(27) }$

Step 2 of 2 :

Find the value of the expression

$\displaystyle \sf{ log_{49}(16807) - log_{9}(27) }$

$\displaystyle \sf{ = \frac{log \: 16807}{log \: 49} - \frac{log \: 27}{log \: 9} }$

$\displaystyle \sf{ = \frac{log \: {7}^{5} }{log \: {7}^{2} } - \frac{log \: {3}^{3} }{log \: {3}^{2} } }$

$\displaystyle \sf{ = \frac{5 \: log \: 7}{2 \: log \: 7} - \frac{3 \: log \: 3}{2 \: log \: 3} }$

$\displaystyle \sf{ = \frac{5 }{2 } - \frac{3 }{2 } }$

$\displaystyle \sf{ = \frac{5 - 3 }{2 } }$

$\displaystyle \sf{ = \frac{2 }{2 } }$

$\displaystyle \sf{ = 1 }$

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