Question

log(5+2root6) to the base root2 + root3


ans is 2 pls explain the solution of the above problem

Answer 1

i hope u will got it...

Answer 2

Concept

There are certain rules based on which logarithmic operations can be performed. The names of these rules are:

• Product rule

• Division rule

• Change of base rule

and many other rules

Given

We have been given a log equation $log_{\sqrt{2} +\sqrt{3} } \ (5+2\sqrt{6)}$ .

Find

We are asked to determine the value of the given log equation .

Solution

It is given that $log_{\sqrt{2} +\sqrt{3} } \ (5+2\sqrt{6)}$ .

By using the property of log which is given by

$log_ab=\frac{log_eb}{log_ea}$

It can be written as

$log_{\sqrt{2} +\sqrt{3} } \ (5+2\sqrt{6)}=\frac{log_e(5+2\sqrt{6)} }{log_e (\sqrt{2} +\sqrt{3}) }$

Multiplying and dividing it by 2 , we get

$\frac{2log_e(5+2\sqrt{6)} }{2log_e (\sqrt{2} +\sqrt{3}) }$

By using the property of log which is given by

$nlog_ax=log_ax^n$

We get

$\frac{2log_e(5+2\sqrt{6)}}{log_e (\sqrt{2} +\sqrt{3})^2 }$

Using the identity $(a+b)^2=a^2+b^2+2ab$ in the denominator, we get

$\frac{2log_e(5+2\sqrt{6)}}{log_e(5+2\sqrt{6)}}=2$

Therefore , the answer of given log equation is 2 .

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