Question

Solve the equation. (Enter your answers as a comma-separated list.)x210x − 6x10x = 27(10x)x =

Answer 1

x = -3, 9

Step-by-step explanation:

First, let us divide both sides of the equation by 10^x; this gives,

`(x^210^x-6x*10^x)/(10^x)=(27*10^x)/(10^x)`
`\Rightarrow x^2-6x=27`

subtracting 27 from both sides gives

`x^2-6x-27=0`

The left-hand side can be factored as

`(x-9)(x+3)=0`

which gives us two further equations

`\begin{gathered} x-9=0 \\ \boxed{x=9.} \end{gathered}`
`\begin{gathered} x+3=0 \\ \Rightarrow\boxed{x=-3.} \end{gathered}`

Hence, the two solutions we get are x = 9 and x = -3.