Question

4.5
score: 20/24 answered: 20/24
question 21
solve the equation for ( x ). answer exactly.
( 4 ln (x + 1) = 12 )
( x = )
question help: video ebook message instructor

Explanation:

Step1: Isolate the natural logarithm term

Divide both sides of the equation \(4\ln(x + 1)=12\) by \(4\).

$$
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$$

Step2: Use the property of logarithms

Since \(\ln a=b\) is equivalent to \(a = e^{b}\) (where \(a=x + 1\) and \(b = 3\)), we can rewrite the equation.

$$x+1=e^{3}$$

Step3: Solve for \(x\)

Subtract \(1\) from both sides of the equation \(x+1=e^{3}\).

$$x=e^{3}-1$$

Answer:

\(x = e^{3}-1\)