7 The solution to the equation \( 5 e^{x+2}=7 \) is
(1) \( -2+\ln \left(\frac{7}{5}\right) \)
(3) \( \frac{-3}{5} \)
(2) \( \left(\frac{\ln 7}{\ln 5}\right)-2 \)
(4) \( -2+\ln (2) \)

Answer

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Answer

Solve for x: \( x = -2 + \ln \left(\frac{7}{5}\right) \)

Steps

Step 1 ：Divide both sides by 5: \( e^{x+2} = \frac{7}{5} \)

Step 2 ：Apply logarithm with base e: \( x+2 = \ln \left(\frac{7}{5}\right) \)

Step 3 ：Solve for x: \( x = -2 + \ln \left(\frac{7}{5}\right) \)