Problem
\[ 7^{x+3}=1705 \] The solution set expressed in terms of loganithms is $\left\{\prod\right\}$. (Use a comma to separate answers as needed. Simplify your answer. Use integers or fractions for any numbers in the expression. Use In for natural logarithm and log for common logarithm.) Now use a calculator to obtain a decimal approximation for the solution. The solution set is $\{\square$. (Use a comma to separate answers as needed. Round to two decimal places as needed.)
Solution
Step 1 ：Given the equation \(7^{x+3}=1705\)
Step 2 ：Convert the equation into logarithmic form using the property of logarithms that states \(log_b(a^x) = x*log_b(a)\)
Step 3 ：Isolate x by subtracting 3 from both sides of the equation
Step 4 ：Calculate x to obtain a decimal approximation
Step 5 ：\(x = 0.8240822133181109\)
Step 6 ：Round to two decimal places as needed
Step 7 ：Final Answer: \(\boxed{0.82}\)
