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\(\newcommand{\amp}{&}\)

The first step for solving each equation below is incorrect. Replace it with the correct step.

$\begin{aligned} 6(5^{3t})\amp=20\\ \color{gray}{(\log 6)(\log 5^{3t})}\amp=\color{gray}{\log {20}}\amp\amp \color{green}{\text{(Wrong!)}} \end{aligned}$
Instead, the first step should be
$5^{3t} = \frac{20}{6}$
$18t =\log_5 20$
$30^{3t}=20$

$\begin{aligned} t \log 8\amp=\log{53}\\ \color{gray}{t}\amp=\color{gray}{\log {\dfrac{53}{8}}}\amp\amp \color{green}{\text{(Wrong!)}} \end{aligned}$
Instead, the first step should be
$t=\frac{53}{8}$
$t = 8^{53}$
$t = \frac{\log 53}{\log 8}$

$\begin{aligned} 12(10)^{-0.06t}\amp=192\\ \color{gray}{120^{-0.06t}}\amp=\color{gray}{192}\amp\amp \color{green}{\text{(Wrong!)}} \end{aligned}$
Instead, the first step should be
$(\log 12)\left(\log 10^{-0.06t}\right)=\log 192$
$10^{-0.72t} = 192$
$10^{-0.06t} = \frac{192}{12}$

$\begin{aligned} \log x +\log {(x-2)}\amp=3 \\ \color{gray}{x + (x-2)}\amp=\color{gray}{10^3}\amp\amp \color{green}{\text{(Wrong!)}} \end{aligned}$
Instead, the first step should be
$\log 2x-2=3$
$\log{(x(x-2))} = 3$
$\log x + \log x - \log 2 = 3$

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