Question

Consider the exponential equation: 2^(x - 8) - 6 = 41) Convert the exponential equation into logarithmic form.A) x + 8 = log2(10)B) x + 8 = log10(2)C) x - 8 = log2(10)D) x - 8 = log10(2)2) Solve the equation for x using logarithmic form.A) x = In(2)/In(10) + 8B) x = In(10)/In(2) + 8C) x = In(2)/In(10) - 8D) x = In(10)/In(2) - 8

Answer 1

Answer:

(a) The correct option is C

`x-8=\log _210`

(b) The correct option is B

`x=(\log10)/(\log2)+8`

Step-by-step explanation:

Given the expression:

`2^((x-8))-6=4`

To write this in logarithmic form, we first add 6 to both sides of the equation

`\begin{gathered} 2^((x-8))=4+6=10^{} \\ 2^((x-8))=10 \\ \text{This means} \\ x-8=\log _210 \end{gathered}`

From

`2^((x-8))=10`

Take logarithm of both sides

`\begin{gathered} \log 2^((x-8))=\log 10 \\ (x-8)\log 2=\log 10 \\ x-8=(\log10)/(\log2) \\ \\ x=(\log 10)/(\log 2)+8 \end{gathered}`