Question

What is the solution set for x in log4(x+5)+log4x=log4 14

Answer 1

`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!