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3 years ago

Somebody plz help on this real quick

Mathematics

1 answer:

Dennis_Churaev [7]3 years ago

6 0

★ Logarithmic Reductions ★

$3 + 4 {e}^{x + 1} = 11 \\ 4 {e}^{x + 1} = 11 - 3 \\ 4 {e}^{x + 1} = 8 \\ {e}^{x + 1} = 2 \\ applying \: log_{e} \: to \: both \: the \: sides \\x + 1 = ln2 \\ x = ln2 \: - 1$

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Sliva [168]

Option A : $x=3.86$ is the solution of the equation.

Explanation:

The equation is $5+8 \ln x=15.8$

To determine the value of x, let us simplify the equation.

Subtracting 5 from both sides of the equation, we have,

$5+\ 8 \ ln \ x-5=15.8-5$

Simplifying, we get,

$8 \ ln \ x= 10.8$

Now , dividing both sides of the equation by 8, we get,

$\ ln \ x=1.35$

Using the logarithmic definition that if $\log _{a}(b)=c$ then $b=a^{c}$

Thus, rewriting the above expression $\ ln \ x=1.35$ using the logarithmic definition, we have,

$\ln \ x =1.35$ ⇒ $x=e^{1.35}$

Substituting the value of $e^{1.35}$=3.85742...$ , we get,

$x=3.85742 \ldots$

Rounding off the answer to two decimal places, we get,

$x=3.86$

Hence, the solution of the equation is $x=3.86$

Therefore, Option A is the correct answer.

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