Solve for \( x \), rounding to the nearest hundredth. \[ 201 \cdot 2^{x}=67 \]

Solve the equation \( 201 \cdot 2^{x}=67 \). Solve the equation by following steps: - step0: Solve for \(x\): \(201\times 2^{x}=67\) - step1: Divide both sides: \(\frac{201\times 2^{x}}{201}=\frac{67}{201}\) - step2: Divide the numbers: \(2^{x}=\frac{1}{3}\) - step3: Take the logarithm of both sides: \(\log_{2}{\left(2^{x}\right)}=\log_{2}{\left(\frac{1}{3}\right)}\) - step4: Evaluate the logarithm: \(x=\log_{2}{\left(\frac{1}{3}\right)}\) - step5: Simplify: \(x=-\log_{2}{\left(3\right)}\) The solution to the equation \(201 \cdot 2^{x}=67\) is \(x = -\log_{2}{(3)}\). To round this value to the nearest hundredth, we can calculate it as follows: \[ x = -\log_{2}{(3)} \approx -1.58496 \] Rounded to the nearest hundredth, the value of \(x\) is approximately -1.58.