The initial expression is
[tex]\log _8(28k-20)+15=18[/tex]
Then
[tex]\Rightarrow\log _8(28k-20)=3[/tex]
Remember the definition of the logarithmic function
[tex]\log _b(x)=y\Leftrightarrow b^y=x[/tex]
In our case,
[tex]\begin{gathered} \log _8(28k-20)=3 \\ \Leftrightarrow8^3=28k-20 \end{gathered}[/tex]
Solving for k:
[tex]\begin{gathered} 512+20=28k \\ \Rightarrow28k=532 \\ \Rightarrow k=19 \end{gathered}[/tex]
The answer is k=19
