Question

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

Answer 1

`x = (3\log 5 + \log 6)/(\log 5 - 4\log 6)`

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 =((-\log 6-3\log 5))/((4\log 6-\log 5))\\ \textrm{Removing minus sign common from numerator and denominator we get}\\\therefore x =(-(\log 6+3\log 5))/(-(-4\log 6+\log 5))\\\\\therefore x =((3\log 5+\log 6))/((\log 5-4\log 6))\\\\\textrm{As Required}`