6. Exponential and Logarithmic Functions

Introduction to Logarithms

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Multiple Choice

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

$\log\left(x+3\right)=9$

$\ln\left(x+3\right)=9$

$\ln9=x+3$

$\log_9x=e^3$

Verified step by step guidance

Identify the given exponential equation: e^9 = x + 3.

Recall the relationship between exponential and logarithmic forms: If a^b = c, then log_a(c) = b.

Apply this relationship to the given equation: e^9 = x + 3 can be rewritten in logarithmic form as ln(x + 3) = 9.

Understand that 'ln' denotes the natural logarithm, which is the logarithm to the base e.

Verify the conversion by checking that the logarithmic form ln(x + 3) = 9 correctly represents the original exponential equation e^9 = x + 3.

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Change the following exponential expression to its equivalent logarithmic form.e9=x+3e^9=x+3e9=x+3