Logarithmic and Exponential Equations Score: 3/10 Answered: 3/10 square Solve for 2: 2^x=23 The exact solution (using logarithms) is: z = x=square The approximate answer,rounded to 4 decimal places, is: z = x=square

To solve the equation $2^x = 23$, we can take the logarithm of both sides of the equation. <br /><br />Taking the logarithm of both sides, we get:<br /><br />$\log(2^x) = \log(23)$<br /><br />Using the property of logarithms that $\log(a^b) = b \log(a)$, we can simplify the left side of the equation:<br /><br />$x \log(2) = \log(23)$<br /><br />Now, we can solve for $x$ by dividing both sides of the equation by $\log(2)$:<br /><br />$x = \frac{\log(23)}{\log(2)}$<br /><br />This is the exact solution using logarithms. To find the approximate answer, we can use a calculator to evaluate the expression:<br /><br />$x \approx \frac{\log(23)}{\log(2)} \approx 4.5632$<br /><br />Therefore, the exact solution is $x = \frac{\log(23)}{\log(2)}$, and the approximate answer, rounded to 4 decimal places, is $x \approx 4.5632$.