Solve for x 2^x*8^(-x)=4^x

Problem

2^x⋅8^(−x)=4^x

Solution

1. Rewrite all terms using a common base of 2

8=2^3

4=2^2

2. Substitute these values into the original equation.

2^x⋅(2^3)^(−x)=(2^2)^x

3. Apply the power of a power rule, which states (a^m)^n=a^(m*n)

2^x⋅2^(−3*x)=2^(2*x)

4. Apply the product rule for exponents, which states a^m⋅a^n=a^(m+n) to the left side.

2^(x−3*x)=2^(2*x)

2^(−2*x)=2^(2*x)

5. Equate the exponents since the bases are equal.

−2*x=2*x

6. Solve for x by moving all terms to one side.

0=4*x

x=0

Final Answer

2^x⋅8^(−x)=4^x⇒x=0

Want more problems? Check here!