Answer:
x=3
Step-by-step explanation:
We are given the equation
[tex]log5x=log(2x+9)[/tex]
This can be rewritten as
[tex]log5x-log(2x+9)=0[/tex]
Now using the quotient rule for logarithms we can combine these two
[tex]log(\frac{5x}{2x+9} )=0[/tex]
Next we can remove the log by using an inverse operation
[tex]10^{log(\frac{5x}{2x+9} )} =10^0\\\\\frac{5x}{2x+9}=1[/tex]
Now we can solve for x
[tex]\frac{5x}{2x+9}=1\\\\5x=2x+9\\\\3x=9\\\\x=3[/tex]
