Solve for x in the equation below(all in picture).

x = - 5, x = 2

Step-by-step explanation:

Using the rules of logarithms

log x - log y = log ( )

x = n ⇔ x =

note that log x = x

Given

log (x² + 3x) - log10 = 0, then

log( ) = 0, thus

= = 1 ( multiply both sides by 10 )

x² + 3x = 10 ( subtract 10 from both sides )

x² + 3x - 10 = 0 ← in standard form

(x + 5)(x - 2) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 5 = 0 ⇒ x = - 5

x - 2 = 0 ⇒ x = 2

Solution is x = - 5, x = 2

i’m here for points.