Question

Solve 5(3^2x+1) - 19 = 6. Round your answer to three decimal places.x = ___

Answer 1

We have to solve for x:

`5(3^(2x+1))-19=6`

We first isolate the term 3^(2x+1) as:

`\begin{gathered} 5(3^(2x+1))-19=6 \\ 5(3^(2x+1))=6+19 \\ 5(3^(2x+1))=25 \\ 3^(2x+1)=(25)/(5) \\ 3^(2x+1)=5 \end{gathered}`

We can now apply logarithm with base 3 to both sides of the equation and get:

`\begin{gathered} \log _3(3^(2x+1))=\log _35 \\ 2x+1=\log _35 \\ 2x=\log _35-1 \\ x=(\log _35-1)/(2) \\ x\approx(1.46497-1)/(2) \\ x\approx(0.46497)/(2) \\ x\approx0.232 \end{gathered}`

Answer: x = 0.232