Question

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

Answer 1

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:

$3x\log 5+\log 5=x\log 4-5\log 4,\\ \\3x\log 5-x\log 4=-5\log 4-\log 5,\\ \\x(3\log 5-\log 4)=-5\log 4-\log 5,\\ \\x=\dfrac{-5\log 4-\log 5}{3\log 5-\log 4}=\dfrac{5\log 4+\log 5}{\log 4-3\log 5}.$

Answer: correct choice is D

Answer 2

Answer:

The correct answer option is $x = \frac{5log4+log5}{log4-3log5}$.

Step-by-step 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:

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

$x = \frac{5log4+log5}{log4-3log5}$