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Let's break it down: 100 * 2^(4x) = 15 This equation is equivalent to the following: 2^(4x) = 15 / 100 This simplifies to: 2^(4x) = 0.15 To solve for x, take the natural logarithm (ln) on both sides: 4x * ln(2) = ln(0.15) To solve for x, divide both sides by 4 * ln(2): x = ln(0.15) / (4 * ln(2)) This equation can be calculated to find x with a calculator. However, since logarithms and exponentials are involved, there might not be an exact simple numerical solution. Typically, a round-off value could be provided. A higher mathematics software might be needed in such a case. Also note: This result will be real only if the base of the logarithm, which is 0.15 in this case, is positive. Otherwise, the result will be complex, specifically when the base is negative or zero.

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