Log_(2)(3x - 8) = 6Please show your work!

Question

asked Nov 18, 2023 218k views

1 Answer

Vons · Answer 1 · 2023-11-24T18:53:13+0000

Logarithmic equations

We know that the following relation is satisfied:

$\begin{gathered} \log _ab=c \\ a^c=b \end{gathered}$

We use this relation in the given formula:

$\begin{gathered} \log _2(3x-8)=6 \\ \downarrow \\ 2^6=3x-8 \end{gathered}$

Using this equation we can find x:

$\begin{gathered} 2^6=3x-8 \\ \downarrow \\ 64=3x-8 \\ \downarrow \\ 64+8=3x \\ 72=3x \\ (72)/(3)=x \\ 24=x \end{gathered}$

Answer: x = 24