Question

Solve the doubts. There might be multiple solutions. There might be no solution

Answer 1

11) You have the following equation:

`\log _3(2x-7)=4`

In order to determine if the equation has solution. Proceed as follow:

- Use the equation above as the exponent of 3:

`3^(\log _3(2x-7))=3^4`

- Then, by properties of the logarithms, you can cancel out the log_3:

`3^(\log _3(2x-7))=2x-7=3^4`

- Now, consider the second and third member of the previous equation:

`2x-7=3^4`

And solve for x by adding 7 both sides and then by dividing by 2 both sides:

`\begin{gathered} 2x=3^4+7 \\ x=(3^4+7)/(2)=(81+7)/(2)=(88)/(2)=44 \end{gathered}`

Hence, the solution for x = 44