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Question Find the value of xx that satisfies the equation 4+9⋅ln⁡x=15.84+9 \cdot \ln x=15.8, rounded to two decimal places.

Studdy Solution

STEP 1

Assumptions1. The given equation is 4+9⋅ln⁡x=15.84+9 \cdot \ln x=15.8 . The solution to the equation should be rounded to two decimal places.

STEP 2

First, we need to isolate the logarithmic term in the equation. We can do this by subtracting4 from both sides of the equation.
9⋅ln⁡x=15.8−49 \cdot \ln x =15.8 -4

STEP 3

Now, calculate the right-hand side of the equation.
9⋅ln⁡x=15.8−=11.89 \cdot \ln x =15.8 - =11.8

STEP 4

Next, we need to isolate the logarithm itself. We can do this by dividing both sides of the equation by9.
ln⁡x=11.89\ln x = \frac{11.8}{9}

STEP 5

Now, calculate the right-hand side of the equation.
ln⁡x=11.89≈1.31\ln x = \frac{11.8}{9} \approx1.31

STEP 6

To get rid of the natural logarithm, we need to use the property of logarithms that states eln⁡x=xe^{\ln x} = x. We can do this by taking the exponential of both sides of the equation.
eln⁡x=e1.31e^{\ln x} = e^{1.31}

STEP 7

implify the left-hand side of the equation using the property of logarithms.
x=e1.31x = e^{1.31}

STEP 8

Finally, calculate the right-hand side of the equation.
x=e1.31≈3.71x = e^{1.31} \approx3.71Therefore, the solution to the equation is x≈3.71x \approx3.71, which corresponds to option B.

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