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