Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Nov 10, 2023

Solve for $x$ the equation $2(2)^{x}=\frac{1}{8}$ .

STEP 1

Assumptions1. We are solving for the variable x in the equation $()^{x}=\frac{1}{8}$ . . The base of the exponent is, which is a positive real number not equal to1.
3. The equation is in the form of $ab^{x}=c$ , where a, b, and c are constants, and x is the variable we are solving for.

STEP 2

First, we need to isolate the exponential term on one side of the equation. We can do this by dividing both sides of the equation by2.
$2^{x}=\frac{1}{8} \div2$

STEP 3

Perform the division operation on the right side of the equation.
$2^{x}=\frac{1}{16}$

STEP 4

Now, we can rewrite the right side of the equation as a power of2, since16 is a power of2.
$2^{x}=2^{-4}$

STEP 5

Since the bases on both sides of the equation are the same (2), we can set the exponents equal to each other. This gives us the equation $x=-4$ So, the solution to the equation $2(2)^{x}=\frac{1}{8}$ is $x=-4$ .

Was this helpful?

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Contact Influencer program Policy Terms