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

Question

asked Apr 27, 2023 110k views

1 Answer

Bulkan · Answer 1 · 2023-05-04T16:09:41+0000

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