3. \( \left(2^{x}\right)=0,3 \)

To solve the equation \(2^x = 0.3\), we can use logarithms to find the value of \(x\). Taking the logarithm of both sides of the equation, we have: \[ \log(2^x) = \log(0.3) \] Using the property of logarithms that states \(\log(a^b) = b \cdot \log(a)\), we can simplify the left side of the equation: \[ x \cdot \log(2) = \log(0.3) \] Now, we can solve for \(x\) by dividing both sides of the equation by \(\log(2)\): \[ x = \frac{\log(0.3)}{\log(2)} \] Let's calculate the value of \(x\) using a calculator. Calculate the value by following steps: - step0: Calculate: \(\frac{\log_{10}{\left(0.3\right)}}{\log_{10}{\left(2\right)}}\) - step1: Convert the expressions: \(\frac{\log_{10}{\left(\frac{3}{10}\right)}}{\log_{10}{\left(2\right)}}\) - step2: Use the logarithm base change rule: \(\log_{2}{\left(\frac{3}{10}\right)}\) - step3: Rewrite the expression: \(\log_{2}{\left(3\right)}-1-\log_{2}{\left(5\right)}\) The value of \(x\) is approximately \(-1.736966\).