Question

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

Answer 1

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