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

$x=\frac{\log10}{\log2}+8$

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

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