Solve the equation for the unknown quantity x.
-$2 ^ { 3 x } = 24$
A) $3.06$
B) $1.53$
C) $0.65$
D) $6.88$

Question

Quizplus · Accepted Answer

To solve $2^{3x} = 24$, first express 24 as a power of 2. Since $24 = 2^3 \cdot 3$, and there's no simple way to express the entire right side as a power of 2, we approach it differently. We can rewrite the equation in logarithmic form or use the fact that $2^3 = 8$, but this doesn't directly help in simplifying $2^{3x} = 24$ in a straightforward manner. Instead, we recognize that the equation cannot be directly solved by expressing 24 as a power of 2. We use logarithms to solve for $x$:Given $2^{3x} = 24$, take the logarithm of both sides (using any base, but base 2 or 10 are most common). For simplicity and relevance to the choices given, we'll use the natural logarithm (ln), though the choice of logarithm base does not fundamentally change the approach:$$ln(2^{3x}) = ln(24)$$Using the logarithmic identity $ln(a^b) = b \cdot ln(a)$, we have:$$3x \cdot ln(2) = ln(24)$$Solving for $x$ gives:$$x = \frac{ln(24)}{3 \cdot ln(2)}$$Using a calculator to find the numerical value:$$x \approx 1.53$$Therefore, the correct answer is B, $1.53$.

Solve the Equation for the Unknown Quantity X 23x=242 ^ { 3 x } = 2423x=24

Solve the Equation for the Unknown Quantity X $2 ^ { 3 x } = 24$