Solve the following exponential equation. Express your answer as both an exact expression and a decimal approximation rounded to two decimal places.
\[
8^{\mathrm{x}-9}=1470
\]

Answer
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Step 1 ：Given the equation \(8^{x-9} = 1470\)

Step 2 ：Take the logarithm of both sides to get \((x-9)\log(8) = \log(1470)\)

Step 3 ：Solve for x to get the exact expression \(x = \frac{\log(1470)}{\log(8)} + 9\)

Step 4 ：Substitute the values of \(\log(8) = 0.9030899869919435\) and \(\log(1470) = 3.167317334748176\) into the equation

Step 5 ：Solve for x to get the decimal approximation \(x = 12.507200146574576\)

Step 6 ：Round the decimal approximation to two decimal places to get \(x = 12.51\)

Step 7 ：Final Answer: The exact expression for the solution is \(x = \frac{\log(1470)}{\log(8)} + 9\). The decimal approximation, rounded to two decimal places, is \(\boxed{12.51}\)