Question

1008 logarithm at the base 12√7

Answer 1

this is Ur required result

Answer 2

Therefore the value of $log_{12\sqrt{7} } 1008$ is $2$

Step-by-step explanation:

Given;

$log_{12\sqrt{7} } 1008=?$

∵$1008=2\times2\times2\times2\times3\times3\times7=2^{4} \times 3^{2}\times7$

We can also write like,

$1008=(2^{2}\times3\times\sqrt{7})^{2} =(12\sqrt{7} )^{2}$

∴$log_{12\sqrt{7} }(12\sqrt{7})^{2}$

$=2log_{12\sqrt{7} }(12\sqrt{7})$  (∵$log_{x}x^{a} =alog_{x}x$)

$=2$  (∵$log_{x}x=1$)

∴ The value of $log_{12\sqrt{7} } 1008$ is $2$