Solve for $\mathrm{x}$ :
\[
1+6 \log _{8}(x-5)=15
\]
Round to 3 decimal places.

Answer

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Answer

Final Answer: The solution to the equation is $\boxed{133.000}$

Steps

Step 1 ：Subtract 1 from both sides of the equation to get $6 \log _{8}(x-5)=14$

Step 2 ：Divide both sides by 6 to isolate the logarithm, resulting in $\log _{8}(x-5)=\frac{14}{6}$

Step 3 ：Convert the logarithmic equation to an exponential equation to get $x-5=8^{\frac{14}{6}}$

Step 4 ：Solve for x to get $x=8^{\frac{14}{6}}+5$

Step 5 ：Using a calculator, we find that $x\approx133.000$

Step 6 ：Final Answer: The solution to the equation is $\boxed{133.000}$