Answer:
[tex]x = \frac{3\log 5 + \log 6}{\log 5 - 4\log 6}[/tex]
Step-by-step explanation:
Given:
[tex]6^{(4x+1)}=5^{(x-3)}[/tex]
To Find:
x =?
Solution:
We have Logarithm identity as
[tex]\log a^{b}=b\log a[/tex]
[tex]6^{(4x+1)}=5^{(x-3)}[/tex]
Taking Log on Both the sides we get
[tex]\log 6^{(4x+1)}=\log 5^{(x-3)}\\\\(4x+1)\log 6 =(x-3)\log 5\\\textrm{applying Distributive Property we get}\\4x\log 6 + \log 6=x\log 5-3\log 5\\4x\log 6-x\log 5=-\log 6-3\log 5\\x(4\log 6-\log 5)=(-\log 6-3\log 5)\\\therefore x =\frac{(-\log 6-3\log 5)}{(4\log 6-\log 5)}\\ \textrm{Removing minus sign common from numerator and denominator we get}\\\therefore x =\frac{-(\log 6+3\log 5)}{-(-4\log 6+\log 5)}\\\\\therefore x =\frac{(3\log 5+\log 6)}{(\log 5-4\log 6)}\\\\\textrm{As Required}[/tex]
