Question

Solve 5^3x+1 = 4^x-5 for x

Answer 1

The correct answer option is
`x = (5log4+log5)/(log4-3log5)`.

Explanation:

We are given the following expression for which we have to make
`x` the subject and solve for it:

`5^(3x+1)= 4^(x-5)`

Taking log from both sides to get:

`=log 5(3x+1) = log 4 (x-5)`

Solving the brackets to get:

`3x log5+log 5 = xlog4-5log4`

`3xlog5+log5 = xlog4 -5log4`

Taking
`x` as the common to get:

`x(3log5 - log 4) = -5log4 - log5`

`x = (5log4+log5)/(log4-3log5)`

Answer 2

For the equation
`5^(3x+1)=4^(x-5)` take the
`\log` from both sides:

`\log 5^(3x+1)=\log 4^(x-5),\\ \\(3x+1)\log 5=(x-5)\log 4.`

Find x:

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

Answer: correct choice is D