\(log_ {4} (x+5) + log_4(x) = log_4(14)\)
For logs with same base :
\(log_b(f(x)) + log_b(g(x)) = log_b(f(x)*g(x))\)
\(Log_4(x+5) + log_4(x) =log_4((x+5)x)\)
\(log_4((x+5) = log_4(14)\)
When the logs have the same base :
\(log_b(f(x)) = log_b(g(x))\)
\(F(x) = g(x)\)
For \(log_4((x+5)x) = log_4(14)\)
Solve \((x+5)x = 14\)
expand
\((x+5)x = x^2 + 5x\)
\(x^2+5x+14\)
\((x-2)(x+7) = 0\)
\(x = 2 , x = - 7\)
Therefore, the final solution : \(x = 2\)
hope this helps!
