question solve for the exact value of x. 5 ln(2x + 5) - 14 = 16

Explanation:

Step1: Isolate the logarithmic term

Add 14 to both sides of the equation: [5\ln(2x + 5)=16 + 14] [5\ln(2x + 5)=30]

Step2: Solve for the natural - logarithm term

Divide both sides by 5: [\ln(2x + 5)=\frac{30}{5}] [\ln(2x + 5)=6]

Step3: Convert the logarithmic equation to an exponential equation

Since (\ln a=b) is equivalent to (e^{b}=a), we have: [e^{6}=2x + 5]

Step4: Solve for (x)

Subtract 5 from both sides: [2x=e^{6}-5] Divide both sides by 2: [x=\frac{e^{6}-5}{2}]

Answer:

(x=\frac{e^{6}-5}{2})