Question

Please help ASAP! 20 points Step by step is you can

Answer 1

Answer:

$x = \frac{3\log 5 + \log 6}{\log 5 - 4\log 6}$

Step-by-step explanation:

Given:

$6^{(4x+1)}=5^{(x-3)}$

To Find:

x =?

Solution:

We have Logarithm identity as

$\log a^{b}=b\log a$

$6^{(4x+1)}=5^{(x-3)}$

Taking Log on Both the sides we get

$\log 6^{(4x+1)}=\log 5^{(x-3)}\\\\(4x+1)\log 6 =(x-3)\log 5\\\textrm{applying Distributive Property we get}\\4x\log 6 + \log 6=x\log 5-3\log 5\\4x\log 6-x\log 5=-\log 6-3\log 5\\x(4\log 6-\log 5)=(-\log 6-3\log 5)\\\therefore x =\frac{(-\log 6-3\log 5)}{(4\log 6-\log 5)}\\ \textrm{Removing minus sign common from numerator and denominator we get}\\\therefore x =\frac{-(\log 6+3\log 5)}{-(-4\log 6+\log 5)}\\\\\therefore x =\frac{(3\log 5+\log 6)}{(\log 5-4\log 6)}\\\\\textrm{As Required}$