Question

Solve. Check for extraneous solutions. There might be no solution or there might be 2

Answer 1

Recall that:

$\log _ba=\text{log}_bc\text{ }\Leftrightarrow\text{ a=c.}$

Therefore,

$(4n-7)=-3n\text{.}$

Solving the above equation for n we get:

$\begin{gathered} 4n-7=-3n, \\ 4n+3n=7, \\ 7n=7, \\ n=1. \end{gathered}$

Now, recall that the logarithm of a negative number is not defined. If n=1, then -3n=-3<0, therefore there are no solutions.

Answer: No solution.