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Hello, I need some assistance with this precalculus homework question, please?HW Q3

Hello, I need some assistance with this precalculus homework question, please?HW Q-example-1
User Sabine
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1 Answer

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Step-by-step explanation:

Given:

We are given the following information;


2^(-x)=4.5

Required:

We are required to find the value of x (that is, the solution to this equation).

Step-by-step solution;

To do this we would re-write this equation by applying the law of exponents, which is as follows;


\begin{gathered} If: \\ f(x)=g(x) \\ Then: \\ ln(f(x))=ln(g(x)) \end{gathered}

With this, we will take the natural log of both sides of the equation;


ln(2^(-x))=ln(4.5)

Next we, take the left side of the equation and apply the law of logs, as shown below;


log_ba^x=xlog_ba

Therefore, we can refine the left side;


ln(2^(-x))=-xln2

We can now re-write the entire equation as shown below;


-xln2=ln4.5

Divide both sides of the equation by ln(2);


(-xln2)/(ln2)=(ln4.5)/(ln2)
-x=(ln(4.5))/(ln(2))

Multiply both sides of the equation by negative 1;


x=-(ln(4.5))/(ln(2))

We now have the exact answer for x.

To solve for the value of x rounded to 3 decimal places;


x=-(ln(4.5))/(ln(2))

With the use of a calculator, we would now have;


x=-(1.504077)/(0.693147)
x=-2.16992

We can round this to 3 decimal places and we'll have;


x=-2.169

Therefore;

ANSWER:


\begin{gathered} (1) \\ A:The\text{ }solution\text{ }set\text{ }is:x=-(ln(4.5))/(ln(2)) \end{gathered}
\begin{gathered} (2) \\ A:The\text{ }solution\text{ }set\text{ }is:x=-2.169 \end{gathered}

User TryHarder
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