Solve 10^x=15.67 for x. Give both the exact answer and the decimal approximation to the nearest hundredth. If you need to use a logarithm to solve, use log. Exact answer: square Decimal approximation: square

To solve the equation $10^{x}=15.67$ for $x$, we can take the logarithm of both sides of the equation.<br /><br />Taking the logarithm of both sides, we have:<br /><br />$\log(10^{x}) = \log(15.67)$<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 />$x\log(10) = \log(15.67)$<br /><br />Since $\log(10) = 1$, we can further simplify the equation:<br /><br />$x = \log(15.67)$<br /><br />Therefore, the exact answer is $x = \log(15.67)$.<br /><br />To find the decimal approximation, we can use a calculator to evaluate $\log(15.67)$:<br /><br />$x \approx 1.20$<br /><br />Therefore, the decimal approximation is $x \approx 1.20$.