Change the following exponential expression to its equivalent logarithmic form.
$e^9=x+3$

• A. $\(\log\]\left\)(x+3\(\right\))=9$
• B. $\(\ln\]\left\)(x+3\(\right\))=9$
• C. $\(\ln\)9=x+3$
• D. $\(\log\)_9x=e^3$

Answer: (B)

Verified step by step guidance

1. Identify the given exponential equation: e^9 = x + 3.
2. Recall the relationship between exponential and logarithmic forms: If a^b = c, then log_a(c) = b.
3. Apply this relationship to the given equation: e^9 = x + 3 can be rewritten in logarithmic form as ln(x + 3) = 9.
4. Understand that 'ln' denotes the natural logarithm, which is the logarithm to the base 'e'.
5. Verify the conversion by checking that the logarithmic form ln(x + 3) = 9 correctly represents the original exponential equation e^9 = x + 3.