Question

Solve. There might be 2 solutions or no solution. Check for extraneous solutions

Answer 1

The initial expression is

`\log _8(28k-20)+15=18`

Then

`\Rightarrow\log _8(28k-20)=3`

Remember the definition of the logarithmic function

`\log _b(x)=y\Leftrightarrow b^y=x`

In our case,

`\begin{gathered} \log _8(28k-20)=3 \\ \Leftrightarrow8^3=28k-20 \end{gathered}`

Solving for k:

`\begin{gathered} 512+20=28k \\ \Rightarrow28k=532 \\ \Rightarrow k=19 \end{gathered}`

The answer is k=19