Please help me solve this equation.

Question

log[2](3)+log[2](x)=log[2](5)+log[2](x-2)

1. Solve equation by setting up algebraically.
2. Use appropriate properties of Logarithm to reduce the number of logarithmic terms to only one.
3. Solve logarithmic equation.

Answer 1

log[2](3)+log[2](x)=log[2](5)+log[2](x-2)
=>
log[2](3*x) = log[2](5*(x-2))
=>
3x=5(x-2)
=>
5x-3x=5*2
=>
2x=10
=>
x=5

Check by putting x into the original equation and see if it balances.