Question

Solve the log equations

Answer 1

Formula used:

`\sf\\\\(i)\ log_a(x)+log_a(y)=log_a(xy)\\\\(ii)\ a^(log_a(x))=x`

Step-by-step explanation:

`\sf\\(a)\ log(x)+log(x+2)=log(x+6)\\or,\ log\{x(x+2)\}=log(x+6)\\or,\ x^2+2x=x+6\\or,\ x^2+x-6=0\\or,\ x^2+3x-2x-6=0\\or,\ x(x+3)-2(x+3)=0\\or,\ (x-2)(x+3)=0\\or,\ x=2\ or\ -3\\x=-3\textsf{ is not possible as log(x) and log(x+2) will not be real numbers.}`

`\sf\\\textsf{The answer for question no. b is given in the image.}`

Answer 2

Hey! I have attached my work for these equations.