Question

Or what value of x does 4x=(1/8)^x+5?
–15
–3
3
15

Answer 1

B, -3

Explanation:

Answer 2

x = -3

Explanation:

`4^x=\left((1)/(8)\right)^(x+5)\qquad\text{use}\ a^(-1)=(1)/(a)\\\\4^x=(8^(-1))^(x+5)\\\\(2^2)^x=\bigg((2^3)^(-1)\bigg)^(x+5)\qquad\text{use}\ (a^n)^m=a^(nm)\\\\2^(2x)=2^(-3(x+5))\iff2x=-3(x+5)\qquad\text{use the distributive property}\\\\2x=-3x-15\qquad\text{add}\ 3x\ \text{to both sides}\\\\5x=-15\qquad\text{divide both sides by 5}\\\\x=-3`