Use main properties of powers
- [tex](a^m)^n=a^{m\cdot n};[/tex]
- [tex]\dfrac{1}{a^n}=a^{-n}[/tex]
to simplify given equation.
1.
[tex]4^x=(2^2)^x=2^{2x}.[/tex]
2.
[tex]\left(\dfrac{1}{8}\right)^{x+5}=\left(\dfrac{1}{2^3}\right)^{x+5}=(2^{-3})^{x+5}=2^{-3x-15}.[/tex]
3. Then the equation is
[tex]2^{2x}=2^{-3x-15}.[/tex]
The bases are the same, so equate the powers:
2x=-3x-15,
2x+3x=-15,
5x=-15,
x=-3.
Answer: for x=-3.
