Question

please solve this question and please send the photo of the solution ​

Answer 1

To find x in:-

$\small \mathtt{ log_{4}(2log_{3}(1 + log_{2}(1 + 3log_{3}x)=\frac{1}{2} }$

Solution:-

Using property of log.

$\mathtt{ 2 log_{3}(1 + log_{2}(1 + 3 log_{3}x) = {4}^{\frac{1}{2} }}$

$\divideontimes \mathtt{\: 2 log_{3}(1 + log_{2}(1 + 3 log_{3}x) = 2}$

$\divideontimes \mathtt{\: log_{3}(1 + log_{2}(1 + 3 log_{3}x) = \frac{2}{2} }$

$\divideontimes \mathtt{\: log_{3}(1 + log_{2}(1 + 3 log_{3}x) = 1}$

$\divideontimes \mathtt{\: 1 + log_{2}(1 + 3 log_{3}x) = {3}^{1}}$

$\divideontimes \: \mathtt{ log_{2}(1 + 3 log_{3}x) = 3 - 1}$

$\divideontimes \: \mathtt{ log_{2}(1 + 3 log_{3}x) = 2}$

$\divideontimes \: \mathtt{1 + 3 log_{3}x= {2}^{2}}$

$\divideontimes \: \mathtt{ 3 log_{3}x= 4 - 1}$

$\divideontimes \: \mathtt{ log_{3}x= \frac{3}{3}}$

$\divideontimes \: \mathtt{ log_{3}x= 1}$

$\divideontimes \: \: \: \: \: \mathtt{ x= {3}^{1} }$

$\huge\mathtt {{\divideontimes \: x= 3}}$