MATH SOLVE

4 months ago

Q:
# solve the equation log(5x)-log(x-3)=1

Accepted Solution

A:

Answer:x = 6Step-by-step explanation:Using the rules of logarithms• log x - log y ⇔ log ([tex]\frac{x}{y}[/tex] )• [tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]Givenlog(5x) - log(x - 3) = 1log ( [tex]\frac{5x}{x-3}[/tex] ) = 1, then[tex]\frac{5x}{x-3}[/tex] = [tex]10^{1}[/tex] = 10 ( cross- multiply )10(x - 3) = 5x10x - 30 = 5x ( subtract 5x from both sides )5x - 30 = 0 ( add 30 to both sides )5x = 30 ( divide both sides by 5 )x = 6