Question

Solve f (x) = 32^x+6•1/2 = 8^x-1

Answer 1

Option B: The value of x is -16

Explanation:

Given that the equation $f(x)=32^{x+6} \cdot \frac{1}{2}=8^{x-1}$

We need to determine the value of x.

Let us substitute f(x) = 0, then we have,

$32^{x+6} \cdot \frac{1}{2}=8^{x-1}$

Now, we shall determine the value of x.

The term $8^{x-1}$ can be written as $\left(2^{3}\right)^{x-1}$

Hence, we have,

$32^{x+6} \cdot \frac{1}{2}=\left(2^{3}\right)^{x-1}$

Also, the term $32^{x+6}$ can be written as $\left(2^{5}\right)^{x+6}$

Thus, we have,

$\left(2^{5}\right)^{x+6} \frac{1}{2}=\left(2^{3}\right)^{x-1}$

Applying the exponent rule, $\left(a^{b}\right)^{c}=a^{b c}$, we have,

   $2^{5(x+6)} \cdot \frac{1}{2}=2^{3(x-1)}$

$2^{5(x+6)} \cdot 2^{-1}=2^{3(x-1)}$

If $a^{f(x)}=a^{g(x)}$ then $f(x)=g(x)$

$5(x+6)-1=3(x-1)$

Simplifying, we get,

$5x+30-1=3x-3$

     $5x+29=3x-3$

     $2x+29=-3$

             $2x=-32$

               $x=-16$

Therefore, the value of x is -16

Hence, Option B is the correct answer.