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question: 2x=ax122x = \frac{a^x}{12}

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Full solution

Q. question: 2x=ax122x = \frac{a^x}{12}
  1. Multiply by 1212: First, multiply both sides by 1212 to get rid of the fraction.\newline2x⋅12=ax12⋅12 2x \cdot 12 = \frac{a^x}{12} \cdot 12 \newline24x=ax 24x = a^x
  2. Take Natural Logarithm: Next, we need to solve for x x . This is a transcendental equation, which means we might need to use logarithms or numerical methods. Let's take the natural logarithm of both sides.\newlineln⁡(24x)=ln⁡(ax) \ln(24x) = \ln(a^x)
  3. Simplify Right Side: Using the properties of logarithms, we can simplify the right side.\newlineln⁡(24x)=xln⁡(a) \ln(24x) = x \ln(a)
  4. Isolate x: Now, isolate x x . Divide both sides by ln⁡(a) \ln(a) .\newlineln⁡(24x)ln⁡(a)=x \frac{\ln(24x)}{\ln(a)} = x
  5. Use Numerical Methods: This equation is still tricky because x x is inside the logarithm on the left side. We might need to use numerical methods or graphing to find the exact value of x x . For now, let's leave it in this form.

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