Question

the logarithm of 1728 to the base 2 root 3 is.

Answer 1

hey mate

here is your answer

log of 1728 to the 2√3

log 2√3 base 1728

log 2√3 base 12³

log 2√3 base (2²*3)³

log 2√3 base (2²*(√3)²)³

log 2√3 base (2√3)^2*3

6 log 2√3 base 2√3

6 is the answer.

hence, second option is right

Answer 2

Answer:

Value of given expression is 6.

Step-by-step explanation:

Given expression:

$log_{2\sqrt{3}}\,1728$

To find: Value of the given expression.

Consider,

$log_{2\sqrt{3}}\,1728$

$=log_{2\sqrt{3}}\:(2^6\times3^3)$

$=log_{2\sqrt{3}}\,(2^6\times3^3)$

Now, to match it with base.

$=log_{2\sqrt{3}}\,(2^6\times((\sqrt{3})^2)^3)$

$=log_{2\sqrt{3}}\,(2^6\times(\sqrt{3})^6)$

$=log_{2\sqrt{3}}\,(2\sqrt{3})^6$

$=6\times log_{2\sqrt{3}}\,(2\sqrt{3})$

$=6\times1$

$=6$

Therefore, Value of given expression is 6.