Answer:
x = -3
Step-by-step explanation:
[tex]4^{x}[/tex]=[tex](\frac{1}{8}) ^{x+5}[/tex]
To solve this, we are going to follow the steps below;
First, we should know that [tex]\frac{1}{8}[/tex] = [tex]8^{-1}[/tex]
Therefore our equation can be re-written as [tex]4^{x}[/tex]=[tex](8^{-1} ) ^{x+5}[/tex]
Also, 4 = 2² and 8 = 2³
Thus, our equation can still be re-written as;
[tex]2^{2x}[/tex]=[tex](2^{-3} ) ^{x+5}[/tex]
We can now proceed to open yhe parenthesis
[tex]2^{2x}[/tex]=[tex]2 ^{-3x-15}[/tex]
By the law of indices,the 2 at the left-hand side will cancel-out the 2 at the right-hand side, our equation becomes;
2x = -3x - 15
Add 3x to both-side of the equation
2x + 3x = -3x + 3x - 15
5x = -15
Divide both-side of the equation by 5 to get the value of x
[tex]\frac{5x}{5}[/tex] = [tex]\frac{-15}{5}[/tex]
(At the left-hand side of the equation, 5 will cancel-out 5 while at the right-hand side of the equation -15 will be divided by 5)
x = -3
Therefore the value of x is -3
