Question

Solve each equation. Express irrational solutions in exact form and as a decimal rounded to 3 decimal places. Verify your results using a graphing utility:$8^{6+3x}=4$

Short answer

The solution set of x is:$\left\{-\frac{16}{9}\right\}$

Step-by-step solution

Step 1. Given information 

An equation,$8^{6+3x}=4$

Step 2. Required to find 

Solve the given equation to find x.

Step 3. Solving the equation

Given, $8^{6+3x}=4$

role="math" localid="1646572365203" $\Rightarrow 2^{3(6+3x)}=2^2$

$\Rightarrow 3(6+3x)=2$

$\Rightarrow 18+9x=2$

role="math" localid="1646572555255" $\Rightarrow 9x=2-18$

$\Rightarrow 9x=-16$

$\Rightarrow x=-\frac{16}{9}$