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Isolating the exponential gives \(\displaystyle 8^{x}=83\). Taking the logarithm of both sides gives \(\displaystyle x = \log_{8}(83)\)

Download \(\LaTeX\)

\begin{question}Solve $8^{x} + 19=102$. 
    \soln{9cm}{Isolating the exponential gives $8^{x}=83$. Taking the logarithm of both sides gives $x = \log_{8}(83)$}

\end{question}

Download Question and Solution Environment\(\LaTeX\)

\documentclass{article}
\usepackage{tikz}
\usepackage{amsmath}
\usepackage[margin=2cm]{geometry}
\usepackage{tcolorbox}

\newcounter{ExamNumber}
\newcounter{questioncount}
\stepcounter{questioncount}

\newenvironment{question}{{\noindent\bfseries Question \arabic{questioncount}.}}{\stepcounter{questioncount}}
\renewcommand{\labelenumi}{{\bfseries (\alph{enumi})}}

\newif\ifShowSolution
\newcommand{\soln}[2]{%
\ifShowSolution%
\noindent\begin{tcolorbox}[colframe=blue,title=Solution]#2\end{tcolorbox}\else%
\vspace{#1}%
\fi%
}%
\newcommand{\hideifShowSolution}[1]{%
\ifShowSolution%
%
\else%
#1%
\fi%
}%
\everymath{\displaystyle}
\ShowSolutiontrue

\begin{document}\begin{question}(10pts) The question goes here!
    \soln{9cm}{The solution goes here.}

\end{question}\end{document}

Solve <img class="equation_image" title=" \displaystyle 8^{x} + 19=102 " src="/equation_images/%20%5Cdisplaystyle%208%5E%7Bx%7D%20%2B%2019%3D102%20" alt="LaTeX: \displaystyle 8^{x} + 19=102 " data-equation-content=" \displaystyle 8^{x} + 19=102 " /> .

Isolating the exponential gives <img class="equation_image" title=" \displaystyle 8^{x}=83 " src="/equation_images/%20%5Cdisplaystyle%208%5E%7Bx%7D%3D83%20" alt="LaTeX: \displaystyle 8^{x}=83 " data-equation-content=" \displaystyle 8^{x}=83 " /> . Taking the logarithm of both sides gives <img class="equation_image" title=" \displaystyle x = \log_{8}(83) " src="/equation_images/%20%5Cdisplaystyle%20x%20%3D%20%5Clog_%7B8%7D%2883%29%20" alt="LaTeX: \displaystyle x = \log_{8}(83) " data-equation-content=" \displaystyle x = \log_{8}(83) " />