Question

For what value of x does 4^x=(1/8)^x+5

Answer 1

B

Explanation:

Answer 2

Use main properties of powers

• 
  `(a^m)^n=a^(m\cdot n);`
• 
  `(1)/(a^n)=a^(-n)`

to simplify given equation.

1.

`4^x=(2^2)^x=2^(2x).`

2.

`\left((1)/(8)\right)^(x+5)=\left((1)/(2^3)\right)^(x+5)=(2^(-3))^(x+5)=2^(-3x-15).`

3. Then the equation is

`2^(2x)=2^(-3x-15).`

The bases are the same, so equate the powers:

2x=-3x-15,

2x+3x=-15,

5x=-15,

x=-3.

Answer: for x=-3.