Solve for x log base 5 of 2x+3 = log base 5 of 3

Problem

(log_5)(2*x+3)=(log_5)(3)

Solution

1. Apply the property of equality for logarithmic functions, which states that if (log_b)(M)=(log_b)(N) then M=N

(log_5)(2*x+3)=(log_5)(3)

2*x+3=3

2. Subtract 3 from both sides of the equation to isolate the term containing x

2*x=0

3. Divide both sides by 2 to solve for x

x=0

4. Verify the solution by substituting x=0 back into the original logarithmic expression to ensure the argument is positive.

2*(0)+3=3

(log_5)(3)=(log_5)(3)

Final Answer

(log_5)(2*x+3)=(log_5)(3)⇒x=0

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