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Solve for x: 4^(2x)=92

Solve for xx: 42x=924^{2x}=92

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Full solution

Q. Solve for xx: 42x=924^{2x}=92
  1. Isolate variable xx: First, we need to isolate the variable xx. Start by taking the logarithm of both sides of the equation to simplify the exponent. We'll use the natural logarithm (ln⁡\ln) for this calculation.
  2. Simplify with logarithm: Using the power rule of logarithms, which states ln⁡(ab)=b⋅ln⁡(a)\ln(a^b) = b\cdot\ln(a), we can simplify the left side of the equation.
  3. Divide by 2ln⁡(4)2\ln(4): Now, solve for xx by dividing both sides of the equation by 2ln⁡(4)2\ln(4).
  4. Calculate with calculator: Calculate the values using a calculator for more accuracy.

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