Solve for x log of 5x = log of 2x+9

Problem

(log_)(5*x)=(log_)(2*x+9)

Solution

1. Apply the one-to-one property of logarithms, which states that if (log_)(a)=(log_)(b) then a=b

5*x=2*x+9

2. Subtract 2*x from both sides of the equation to isolate the terms containing x

3*x=9

3. Divide both sides by 3 to solve for x

x=3

4. Verify the solution by checking if the arguments of the logarithms are positive.

5*(3)=15>0

2*(3)+9=15>0

Final Answer

(log_)(5*x)=(log_)(2*x+9)⇒x=3

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