to solve $5(2^{x + 4}) = 15$, first divide each side by $5$.

solve $5(2^{x + 4}) = 15$. round to the nearest thousandth.

$x \approx$

Question

to solve $5(2^{x + 4}) = 15$, first divide each side by $5$.

solve $5(2^{x + 4}) = 15$. round to the nearest thousandth.

$x \approx$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Solving Exponential Equations Algebraically", "Solving Exponential Equations" ], "new_concepts": [], "current_concepts": [ "Solving Exponential Equations Algebraically", "Solving Exponential Equations" ] } ## Isolate the exponential term Using the *Solving Exponential Equations Algebraically* knowledge point $$ \begin{aligned} 5(2^{x+4}) &= 15 \ 2^{x+4} &= 3 \end{aligned} $$ ## Apply logarithms to solve for the exponent Using the *Solving Exponential Equations* knowledge point $$ \begin{aligned} \log_2(2^{x+4}) &= \log_2(3) \ x + 4 &= \frac{\ln(3)}{\ln(2)} \ x &= \frac{\ln(3)}{\ln(2)} - 4 \end{aligned} $$ ## Calculate the numerical value Using the *Solving Exponential Equations* knowledge point $$ \begin{aligned} x &\approx 1.58496 - 4 \ x &\approx -2.41504 \ x &\approx -2.415 \end{aligned} $$ Solve $5(2^{x+4}) = 15$. Round to the nearest thousandth. $x \approx$ -2.415 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Solving Exponential Equations Algebraically" ] }

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QUESTION IMAGE

Question

Explanation:

Isolate the exponential term

Apply logarithms to solve for the exponent

Calculate the numerical value

Answer: