Question

convert $e^x = 9.25$ to logarithmic form and find the value of $x$.

\\(\circ\\) 1.522

\\(\circ\\) 2.921

\\(\circ\\) 2.224

\\(\circ\\) 3.254

Explanation:

Step1: Recall Exponential to Logarithmic Conversion

For an exponential equation \( a^b = c \), the logarithmic form is \( \log_a c = b \). Here, the base \( a = e \), exponent \( b = x \), and \( c = 9.25 \). So the logarithmic form is \( \ln(9.25)=x \) (since \( \log_e c=\ln c \)).

Step2: Calculate the Natural Logarithm

Using a calculator, we find \( \ln(9.25) \). We know that \( \ln(e^x)=x \), and we can compute \( \ln(9.25) \approx 2.224 \) (by using the natural logarithm function on a calculator: \( \ln(9.25) \approx 2.224 \)).

Answer:

2.224 (corresponding to the option with 2.224)