Verified Answer :

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Elsa's answer is incorrect since there is a solution of the given equation. In the given logarithmic problem, we need to simplify the problem by transposing log2(3x+5) in the opposite side. The equation will now be log2x-log2(3x+5)=4. Using properties of logarithm, we further simplify the problem into a new form log (2x/6x+10)=4.  Then transform the equation into base form 10^4=(2x/6x+10) and proceed in solving for x value which is equal to 1.667.

To check weather Elsa is correct, we need to solve the given equation using logarithm properties.

Elsa solution is correct.

Given:

The given equation is as follows.

\(\rm log_2x=log_2(3x + 5) + 4\)

Convert 4 in form of log.

\(\rm log_2x=log_2(3x + 5) + 4log_22\\\rm log_2x=log_2(3x + 5) + log_22^4\)

Use the logarithm property \({\rm log}m+{\rm log}n={\rm log}mn\)

\({\rm log}_2x={\rm log}_2[(3x + 5)\times 16]\\{\rm log}_2x={\rm log}_2(48x+80)\)

Comparing both side.

\(\begin{aligned}x=48x+80\\x-48x=80\\x=\frac{80}{-47} \\x=-\frac{80}{47} \end{aligned}\)

The x value can not be negative because the log is not defined for negative. Thus, Elsa is correct.

Learn more about logarithm property here:

https://brainly.com/question/12049968

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